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Q: How to Axiomize the Notion of "Continuous Space"? EDIT (to clear up controversy and misunderstandings caused by my poor wording): Historically, Riesz's efforts to try and make rigorous a notion of a "continuous space" (as opposed to "discrete ones") were part of some of the movements in mathematics which lead to the establishment of the axioms of topology.
Some people tout topologies as being "the axiomization of the notion of a continuous space". However, they are clearly too general, as I argue below.

What is an appropriate level of axiomization to make rigorous a notion of "continuous space"?

Why do we allow either discrete or trivial topologies in the definition of topology? (if we want it to define "continuous spaces", otherwise there is no issue)
More generally, why do we allow points to be open (the existence of isolated points) or the failure of the T0 axiom (existence of topologically indistinguishable points)? (if we want it to define "continuous spaces", otherwise there is no issue)

Both scenarios could be prevented by addition of the following axioms to the definition of topology:

*

*No point is open

*Every point has a unique neighborhood system

This question is a follow-up to my previous question: Why study non-T1 topological spaces?
The historical motivation for topology, as far as I have read, was to give a rigorous notion to the intuition of a "continuous space". The three axioms commonly used are equivalent to those proposed by Kuratowski, Riesz, and Hausdorff, who were trying to axiomatize "continuous space".
But discrete spaces are the exact opposite of that, and in general allowing isolated points allows the possibility of spaces with "discrete components". It also makes the definition of "limit" unnecessarily complicated. The discrete topology is also equivalent to the power set, so is in effect not a new notion. Also every function from a discrete space is continuous, and any definition of a function at an isolated point is continuous, which goes counter to the expectation that the morphisms of a given category should be "special" functions. Basically discrete topologies gains us no new insights compared to elementary set theory.
Moreover, points not having unique neighborhood systems lead to all sorts of pathologies (for example here: Non-T1 Space: Is the set of limit points closed?), and even the Zariski topology, which is the most pathological commonly used topology of which I am aware, is still in general $T0$.
Finally, any non-$T0$ space should be homeomorphic (I think) to the quotient of the space under the equivalence relation " $x \sim y$ if and only if $x$ and $y$ are topologically indistinguishable".
This question is similar in spirit to this one, but to me it is very clear why we would want to consider non-metric spaces, at least as someone who is interested non-metricizable spaces like those which can occur in functional analysis. I am aware of the notion of continuum, but since the definition requires the space to be metric, and focuses more on compactness than separation axioms and connectedness rather than path-connectedness, I believe it to be the incorrect axiomization of a "continuous space". The existence of indecomposable continua lends credence to this notion, in my view.
However, it seems clear to me that the proper axiomization of a "continuous space" must lie somewhere in between the notion of "metric space" and "topological space", as the former is far too restrictive, and the latter far too general. I would enjoy your thoughts on the matter.
(I want to better axiomize the notion of "continuous space" so as to better facilitate the study of stochastic processes, not that this is directly relevant to the immediate question at hand.)

EDIT:
At least Riesz appeared to have been clearly interested in defining some notion of "continuous space" or "continuum" (excerpt from "History of Topology" on google books (https://books.google.com/books?id=7iRijkz0rrUC&pg=PA212&lpg=PA212&dq=riesz+topology+axioms&source=bl&ots=B_xcnG6StL&sig=EajpOCr3XRUtA9hwqpLwArKLmoY&hl=ru&sa=X&ved=0ahUKEwj3pMPs9ZvNAhVBGFIKHcXmB28Q6AEIJzAC#v=onepage&q&f=false):

In a footnote Riesz criticisms the way in which philosophers have dealt with notions like continuous and discrete and he repeats Russell's remark about the followers of Hegel: «the Hegelian dictum (that everything discrete is also continuous and vice versa) has been tamely repeated by all of his followers. But as to what they meant by continuity and discreteness, they preserved a discrete and continuous silence; […]» (Riesz [147]). The relation of our subjective experience of space and time and mathematical continua is described by Riesz as follows. Mathematical continua possess certain properties of continuity, coherence and condensation. On the other hand, our subjective experience of time is discrete and consists of countable sequences of moments. Systems of subsets of a mathematical continuum can be interpreted as a physical continuum when subsets with common elements are interpreted as undistinguishable and subsets without common elements as distinguishable. Rise [147, p. 111] is an interesting paper in which Riesz, who had read Frechet's work and appreciated it, developed a different theory of abstract spaces, based on the notion of «Verdichtungsstelle», i.e. «condensation point», or as we will translate «limit point». In his theory Riesz succeeded in deriving the Bolzano-Weierstrass Theorem and the Heine-Borel Theorem. We will not discuss this paper. We will restrict ourselves to a shorter paper that was presented by Riesz in 1908 at the International Congress of Mathematicians in Rome. In that paper, «Stetigkeit und Abstract Mengenlehre» (Riesz [148]), concentrates on the characterization of mathematical continua. We will briefly describe some of the ideas the Riesz describes in the paper. As we said, Riesz's basic notion is the notion of a limit point (Verdichtungsstelle).

I'm not asking anyone to agree with Riesz's basic goal (to get a rigorous distinction between "continuous" and "discrete" spaces or time).

To those who might object that the standard three axioms are all that are necessary to define the notions of connectedness and compactness, I have several responses:

*

*Connectedness actually isn't that nice of a property. We could look at the topologist's sine curve or the infinite broom for examples, but for me the fact that there exists a countable, Hausdorff, and connected set implies that topological connectedness is not quite the intuitive connectedness from Euclidean spaces which we want to generalize for an arbitrary "continuous space". In my mind, path connectedness better satisfies this criterion, since every non-trivial T1 path-connected space is uncountable. Path connectedness does provide reasonable properties, although one can object that the definition is somewhat of a tautology ("a space behaves like the real line if it behaves like the real line") and requires the prior construction of the real line in order to define, rather than being constructible from first principles.

*Compactness also isn't very nice unless we are in a Hausdorff space, since otherwise compact sets aren't even closed. Sure $T0$ isn't Hausdorff, but it's certainly a step in the right direction. (Hence why the distinction between "compactness" and "quasicompactness" is so prevalent in algebraic geometry where the non-Hausdorff Zariski topology so frequently comes into play).

*For non-$T0$ spaces, the set of limit points isn't even closed, limits aren't unique or well-defined... the notion of limit so intrinsic to the idea of a "continuous space" clearly requires at least $T0$, if not even $T1$ or $T2$, to function even remotely similarly to intuition.

Related but different: Why the axioms for a topological space are those axioms?
The definition of metric space,topological space
What concept does an open set axiomatise?
Why do we require a topological space to be closed under finite intersection?
https://xorshammer.com/2011/07/09/a-logical-interpretation-of-some-bits-of-topology/
https://mathoverflow.net/questions/19152/why-is-a-topology-made-up-of-open-sets
https://en.wikipedia.org/wiki/Decidability_(logic)#Semidecidability
meaning of topology and topological space
Motivation behind topology
Why is discrete space ``discrete"
Discretizations of Differential, Geometric and Topological Notions
Origins of the modern definition of topology

A: If you didn't allow these two sorts of topology (discrete and trivial,) then if $X$ was a space with topology $\tau$, and $Y\subset X$, you couldn't always define a topology on $Y$.
The most obvious example is that the discrete topology on $\mathbb Z$ is the topology you get by considering $\mathbb Z\subset \mathbb R$ with the usual topology on $\mathbb R$.
It's a little harder to get trivial topologies, since you'd have to start with a non-Hausdorff topology.
I'm guessing there are category-theory reasons, also - that limits or co-limits might fail to exist in the category of topological spaces. But that's possibly more advanced than you need, and I'm not sure it is true.
The original definitions of topology had pretty strong axioms, to match metric spaces more closely.
But then people encountered "spaces" where fewer and fewer of the separation rules were satisfied. But I'm not sure I've ever personally seen a topology used in real math that was not $T_0$.

A: This question is way too tl;dr for me, but one phrase that hasn't been thrown around here, as far as I can tell, is "uniform space," and I wonder if that's one way of getting at what you want from a notion of "continuous space," since it is the topological setting were Cauchy completeness makes sense -- one step up in generality from metric spaces. (See also the nLab page.)
Leaving this as an answer rather than a comment since there are already so many comments.

A: Perhaps topological manifolds are what you're looking for. Every connected topological manifold can be thought of as a "continuous space." If you don't demand connectedness, they can be "discrete." This eliminates examples like $\mathbb{Q}$, for better or worse.
Another possible solution is to just focus on "metrizable" topological spaces, or "completely metrizable" ones. The former allows $\mathbb{Q}$, the latter disallows it. Make sure to allow your metrics to take values in the interval $[0,\infty],$ otherwise your category of metrizable spaces won't have coproducts.
Also, Flagg spaces (he calls them "continuity spaces", but this is a poor choice of phrase) are a generalization of metric spaces in which every topology arises from a suitably chosen metric. So you might find that interesting; I think they're mainly used in computer science.
A general comment: if you're interested in the question of how much generality is needed in the definition of a topological space, its worth learning as much functional analysis as you can, and especially just spending a lot of time thinking about infinite-dimensional function spaces.
For a very different viewpoint on what the axioms of topology ought to be, take a look at the nlab page on convenient categories of topological spaces. The idea is that a good category of spaces should have nice categorial properties, like $\mathbf{Set}$ does. My personal feeling is that we need to generalize, rather than specialize: convergence spaces are imo a very natural and appealing framework in which to formalize topological intuition. You may also be interested in uniform convergence spaces.

A: The notion of a topology being a frame of open sets is described by nice algebraic properties and is well behaved under various constructions. This implies that "topological space" is the sort of mathematical structure that is amenable to study.
(In fact, the idea of a frame of open sets is so nice that there has since spawend a theory of locales which keep the frames but discard the notion of points. This is sometimes called "pointless topology")
This means, if whatever particular kind of thing you want to study can be expressed as a topological space, then usually, the most fruitful way to study it is as a "topological space with additional properties".

A: There was a teacher of mine which used to restrict the definition of continuity to the points of the set which were limit points. Hence, asking if the function $f:\{0 \}\cup [1,2] \to \mathbb{R}$ was continuous was not meaningful to him.
I asked him "why are you restricting it?" He answered (paraphrasing, of course. I don't remember the exact words): "Because continuity is a concept related to the process of limits, it is not quite meaningful to attribute the word 'continuous' to a point to which nothing is converging to." This phrase is quite, quite similar to your "proper axiomatization of a continuous space", whatever that means.
Turns out that later in class he needed to use the continuity of a function which he was restricting. I asked promptly: "Why is this function continuous? You first need to prove that all points of your set are limit points." After some discussion, he conceded on his definition of continuity.
The bottom line is: A lot of times in mathematics, it so happens that grasping to one's psychological comfort only leads to unnecessary hindrance. Making more assumptions than needed will often lead to useless labor, and also to wasted time.

A: Here are my thoughts on this question, and how I would answer it now:
In what follows, I will use "continuous" in the sense of "continuous enough for an analyst to care about it or find it interesting" and not in the sense of "morphism between topological spaces"; the latter sense is obviously much more general. However, I believe the former sense better captures the layperson's intuition of the word continuous, as well as what Riesz was referring to. Indeed, some consider analysis to consist of "precise formulation of intuitive notions of... continuity", or the study of "continuous change". Only the former sense of the term "continuous" makes sense in these contexts, whereas the latter does not.
Functional analysis is often taught as, and to some extent de facto is, a continuation of real and/or complex analysis. To some extent, the distinction is only relevant for elementary analysis, since problems in the field inevitably lead one to consider function spaces.
What unifies these spaces being studied? That they all are topological vector spaces over $\mathbb{R}$ or $\mathbb{C}$, often with multiple compatible/interesting topologies to choose from. (If we want to include the study of manifolds/differential geometry, then one has to abstract further to "spaces which are locally homeomorphic to topological vector spaces over $\mathbb{R}/\mathbb{C}$.)
One might object that one shouldn't need an "algebraic" structure to define spaces which correspond to the intuitive notion of "continuous", and that topological structure should be all that is necessary. However, I have several responses to this:

*

*Remember that the topological notion of continuity doesn't correspond to the intuitive notion conveyed by the use of the word "continuous" in everyday speech.

*We can think of the algebraic condition of being a vector space over $\mathbb{R}$ or $\mathbb{C}$ as meaning that the space "plays nice" with $\mathbb{R}$ and $\mathbb{C}$. Since these two are in some sense the simplest possible spaces for which we don't have to worry about Cauchy sequences not converging, any space that plays nicely with them will be more likely to correspond to our intuition that a Cauchy sequence "should" converge.

*If we want to include function spaces, then we need to restrict ourselves to vector spaces, because almost any function space in which we could possibly be interested in (as an analyst) is a vector space.

*The restriction doesn't matter that much when we generalize to spaces which are "locally homeomorphic to topological vector spaces over $\mathbb{R}/\mathbb{C}$", plus naturally puts in place some of the machinery necessary to have well-defined tangent spaces. And I think tangent spaces also correspond well to our intuitive notion of continuity (which is sometimes called smoothness) - for example, at the point of a cone where there is no well-defined tangent plane, we say that it is "pointy" but not "smooth".

*Remember that being a topological vector space doesn't mean having a mishmash of topological and algebraic structures -- the two structures have to be compatible with each other, which means to some extent that they have to reinforce each other. So to some extent the purpose of the vector space part is to just impose additional topological conditions.

*There are many important topological properties which correspond to our intuitive notion of "continuous" which follow from their (topological) vector space structure, I will outline this in further detail below.

*Empirically speaking, most of the topological counterexamples to the intuitive notion of "continuous space" which I found on $\pi$-base were either not vector spaces (or if they were, they weren't vector spaces over $\mathbb{R}$ or $\mathbb{C}$) or were vector spaces but had a topology which either was not compatible with the vector space structure or was not naturally related to it. This suggested to me that something fundamental was going on here.
The strongest argument, however, for imposing algebraic conditions, is the following:

A group topology is determined by its system of neighborhoods of the identity. In particular, the system of neighborhoods at each point are homeomorphic to one another.

Thus what might seem like an abstract condition actually amounts to an intuitive, almost geometrical one: each point of the space, considered locally, is indistinguishable.
The fact that this isn't true for general topological spaces makes them interesting objects of study; however, it doesn't necessarily correspond to intuitive notions of "continuous".
However, I will add one purely topological condition: a "continuous" space must also be $T1$. This is for at least two reasons:

*

*As I have already argued elsewhere, it is most natural for a space which is "continuous" in the intuitive sense to have points which are closed and no points which are open. This should mean in particular that every point in the space has a unique neighborhood system (is distinguishable in the topology), the set of limit points is closed, and that the space does not rely on any single point for its "continuity" (i.e. we still have an open set when removing any individual point). These assumptions make the space much better behaved from a limit convergence standpoint and also inherently remove many examples of "discrete" or "semi-discrete" spaces from consideration.

*Several very important topological consequences follow only for topological vector spaces which are also $T1$ and it is a safe assumption to make in analysis, hence why many authors (e.g. Rudin) routinely make it.
Let's start deriving the nice properties which will make the crux of my argument.

*

*Any such space is not just $T1$, but actually completely regular and has a uniform structure on it. Both of these are also often considered to correspond to the intuitive notion of continuity; we get them for free based on relatively weak axioms.

*Every such space is not only automatically locally path-connected, but locally arc-connected, since being Hausdorff and locally path-connected imply being locally arc-connected. In other words, it automatically has a bunch of curves (topological 1-manifolds) as subsets, which also corresponds well to our intuitive notion of "continuity".

*Every such space (except for the trivial one) is uncountable, i.e. has "cardinality of the continuum", because any path-connected space consisting of more than two points is uncountable.

*Because the space is Hausdorff, every limit is unique! Hence these spaces are particularly good for studying limits. Every compact subset is also closed in these spaces as a result, again in accordance with intuition.

*This is also already enough structure to define a concept of boundedness: https://en.wikipedia.org/wiki/Bounded_set_(topological_vector_space). While a "continuous space" should be in some sense "deformable", it shouldn't be arbitrarily deformable without changing its "character". Boundedness of sets provides a nice invariant to consider in many contexts.

*Such a space is discrete if and only if it is trivial, which corresponds beautifully with intuition.
All of this without even imposing a metric! Meaning we still get a lot of good properties but still have enough generality consider non-metrizable spaces of interest in analysis (e.g. weak-* topology).
Another good argument for these spaces corresponding to intuition, however, relates to metric spaces. Specifically, these spaces are metrizable if and only if they have countable neighborhood bases. This provides a very simple and easy criterion determining whether or not a space of this type is metrizable, something which does not hold in general. Moreover, this criterion corresponds very nicely to the intuition afforded by considering "balls of radius 1/n and n" which we can use for local neighborhood bases in Euclidean spaces. Finally, every such space of this type which is metrizable is a Baire space by the Baire Category Theorem.
In short, these spaces have via trial and error naturally singled themselves out as the principle objects of study in analysis and differential topology/geometry, and they have most, if not all, of the properties one would associate with an intuitive notion of "continuous space". They also include all of the standard examples which would come to mind, including topological manifolds and all of the most widely-studied function spaces (according to Wikipedia).
See these other questions of mine for more detail: What is the motivation behind the arbitrary union topological axiom?. Note that neither separability nor second-countability hold for these spaces I mentioned in general, and that first-countability holds if and only if the space is metrizable.
Are there any "default" properties which hold for almost all topological spaces in analysis? (The comments are somewhat useful).
https://math.stackexchange.com/questions/1836475/t-f-properties-of-every-non-trivial-topological-vector-space-over-mathbbr
Corollary of the Birkhoff Kakutani Theorem: first countable topological vector spaces
Can Path Connectedness be Defined without Using the Unit Interval? (The answer to this question leads to the argument that path-connectedness is not too unreasonably strong of a property to ask a space to have.)
Is Every (Non-Trivial) Path Connected Space Uncountable?
Why study non-T1 topological spaces? Basically any non-T1 space is not of interest in analysis, except for some operator algebras, but I don't see any strong motivation to want to include all operator algebras/spectra as belonging to the intuitive notion of "continuous space", even if they are useful for studying them.

UPDATE: On p. 36, chapter 2, of Lee's Introduction to Topological Manifolds, it states that

The most important feature of first countable spaces is that is that they are the spaces in which sequences are sufficient to detect most topological properties.

This statement becomes more accurate in the context of continuous spaces, as I have defined them above, as compared to general topological spaces.
For example, a metric space is compact if and only if it is sequentially compact. A continuous space is metrizable if and only if it is first countable. A first countable space is countably compact if and only if it is sequentially compact. Therefore, countable compactness, sequential compactness, and actual compactness all coincide in a continuous space if and only if it is first countable. This accords better with intuition.
An even more ideal result would be to show that a continuous space is a sequential space if and only if it is first-countable. However, I do not know enough about the latter at this time to confirm or deny this. Nevertheless, the usual direction of implication holds, namely that first countable implies sequential, thus sequential continuity and continuity coincide for all metrizable=first-countable continuous spaces.
It would also be nice to find some relationship between continuous spaces and Frechet-Urysohn spaces: sequential continuity vs. continuity.

A: Well, let me try to define something which I think should give a reasonable definition of a "continuous space". The idea is to generalize the notion of path-connectedness so it doesn't rely on a mapping to the real numbers.
Here's my definition:

A topological space $X$ is a continuous space if for any pair of points $x_1,x_2\in X$ there exists a connected subset L with $\{x_1,x_2\}\subset L\subset X$ and a dense total order on $L$ so such the order topology on $L$ coincides with its subset topology.

Also note that every path-connected space fits the definition, as the order on the real line induces an order on the path.

A: This might be a little late to the party, but I highly recommend reading about the Theory of Linear Structures from Tim Maudlin.
Rather than using the notion of an open set as primitive, this theory uses the notion of a Line (essential to this notion is the linear ordering of points). A linear structure is a point set S along with a set of lines L, satisfying certain axioms. The lines contain the information of which points "surround" which, specifying the neighborhood structure, which specifies open set structure, and so on (this theory does employ different ways of expressing concepts using the available info of lines, as opposed to the usual definitions with open sets).
A space is called a continuum if the linear order of every line is dense and complete. Does that help?


Just the other day, I was wondering if they would be doing an update or remake of the classic Tron. Here's the answer. And what movie about video games would work if you didn't want to play it? Check it out.


Sinead O'Connor has resurfaced on social media for the second time in two days since sharing a status update in which she threatened to overdose. Since her suicide scare on Sunday, the singer has posted several updates on Facebook in which she called out members of her family, claiming they came to the hospital to see her while she was unconscious only to leave before she came to. The troubled Irish musician has written yet another post on Facebook, this time crying out to the same family members she previously claimed were "dead" to her.
As was reported by People magazine O'Connor, 48, updated her status again on Monday in which she changed her tune from anger to sadness. The "Nothing Compares 2 U" singer plead with her family to come and face her, asking them to explain "why this is all happening." O'Connor claimed she'd been missing them for several weeks and was now "[utterly] alone." She plead with them not to leave her scared and alone in the hospital and to stop treating her like she was "not loved" and "worth nothing."
"Please why are you doing these things to me?? I need you. I need your love. I can't manage what's been done to me," she wrote. "Come and tell me why this is all happening. Come and tell Me I'm loved ... Been missing you all for weeks. To hear that you were here and left was agony. Now I am [utterly] alone. Please. Please love me. Please come to the hospital and spend time with me and help Fix all this. Please. I'm BEgging you. Don't leave me so frightened and alone. Don't treat me like I'm not loved and am worth nothing. Please. If you love me even a little please come and be with me and help me understand what's happening... Help me [instead] of punishment. Please please I beg you come see me and help."
Earlier that same day O'Connor called out six members of her family online, including her sons. She accused one of the names listed of killing their mother and another of stealing her children from her. O'Connor wrote that she had suffered an unimaginable amount of cruelty at the hands of her family members and others and couldn't take it anymore. She revealed to her Facebook friends that they'd visited her in the hospital, but only while she was unconscious.
That message came one day after the controversial musician sent fans into a frenzy, fearing she had taken her life. In a status update posted on Sunday, O'Connor claimed she was in a hotel, which she had booked under another name, and had "taken an overdose." Fortunately, hours later local police released an update in which they said she had been found "safe and sound."


text:
CTA Productivity Measures and Comparisons
The Civic Federation conducts an analysis of the Chicago Transit Authority's annual proposed budget each year. This analysis includes two measures used to assess CTA's productivity over time: labor cost per actual unlinked passenger trip and operating expense per passenger mile.[1] The data used to calculate the productivity measures are obtained from the annual budget documents.
As discussed in previous years, the labor cost per unlinked passenger trip is a metric in which a lower dollar amount equals higher productivity. In FY2019, productivity is projected to decline as the labor cost increases to $2.35 per unlinked passenger trip, following a five-year trend. This is an increase of $0.09 between FY2018 and FY2019, as well as an increase of $0.41 since FY2015. The chart below presents these trends.
This decrease in productivity is due also to declining ridership. Ridership has fallen by 2.1% on average each year since FY2015, whereas labor costs have increased by 2.3% on average each year. The CTA attributes the decline in ridership to extreme winter weather in FY2015, competition from alternative transit providers such as Uber and Divvy, and low fuel prices from FY2016 to FY2018, which encouraged more car usage.[2]
The chart below illustrates operating expense per passenger mile for bus and rail service between 2012 and 2016, the most recent years for which data is available. Within transit systems, rail service is commonly more cost effective than bus service due to higher ridership on trains. The CTA reports the operating expense for rail service has increased from $0.33 in FY2012 to $0.41 in FY2016. The operating expense for bus service has increased by $0.20 during this period. It dipped from $1.06 in FY2012 to $1.05 in FY2013, before increasing to $1.26 per passenger mile in FY2016.
Chicago's rail system remains the lowest cost among peer cities at $0.41 per passenger mile, $0.27 lower than the highest cost per passenger mile in Washington, D.C. Additionally, Chicago's bus system has a cost of $1.26 per passenger mile, third lowest among its peers and $0.53 lower than the highest cost per passenger mile in New York City. The table below presents this data.
The Civic Federation will be releasing its full analysis of the Chicago Transit Authority's FY2019 Recommended Budget next week.
[1] "Ridership" and "unlinked passenger trips" refer to total number of rides. Each passenger is counted each time that passenger boards a vehicle (bus or rail). CTA President's FY2019 Budget Recommendations, p. 210.
[2] CTA President's FY2019 Budget Recommendations, p. 33.

redpajama_set_name: RedPajamaCommonCrawl


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Employers Cannot Be Forced to Re-Engage Unfairly Dismissed Workers
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To facilitate this, commonly understood and acknowledged digital currencies, such as ECTS credits or university degree certificates, as well as vocabularies like the European Qualifications Framework (EQF) levels and ISCED-F codes for subject areas, are required. Equally necessary are open and ubiquitous documentation templates that allow a thorough and precise interpretation and validation of credentials by any of the above-mentioned stakeholders.
People familiar with open-education practices could immediately say that such templates already exist in the form of open badges. This, of course, is a valid observation, but I would argue that open badges have so far been unable to get traction in higher education because they are a bit "too open" and "too flexible" to be applied in a sector in which formal accreditation and standardisation are crucial components of quality assurance.
So how can we achieve the best of both worlds? That is, how can we establish highly structured and standardised mechanisms of credentialization that are principally open and transparently interoperable?
Certain global trends are clearly urging the production of more open digital credentials. Higher education, for example, is becoming more open and flexible – with joint degree courses and some universities sharing their MOOCs on popular platforms like Coursera and Udacity. Moreover, the labour market's demand for constantly changing and unique sets of knowledge, skills, and competencies is pressing HEIs to pay more attention to issuing credentials that are open, portable, and quick and easy to validate. Best-practice cases of the latter are still rare.
Europass is the still-evolving, go-to online CV template for many job seekers in Europe. It can provide – in addition to a well-structured CV – a Certificate Supplement for people who hold a vocational-education-and-training certificate, as well as other EU-supported documents and self-assessment tools to produce annexes, such as the Europass Language Passport.
The European Qualifications Framework (EQF) indicates the level of various qualifications, but not micro-credentials or those earned through non-formal education.
The European Diploma Supplement provides a standardised template with additional information about a study-programme diploma, but only for degree-level education.
The European Credit Transfer System (ECTS) describes individual learning units in terms of knowledge, skills, responsibility, and autonomy, but it is only used in higher education.
The European Skills, Competences, Qualifications and Occupations (ESCO) database provides a standard terminology of skills, competences, qualifications, and occupations, but these terms are not used or referenced in any of the above-listed tools.
The ReOPEN project developed validated non-formal open-learning practices, allowing for transparent recognition of skills, qualifications, and competences by education providers and employer organisations. It also established instruments (a course template, a learning agreement, and learning-offer- description tools on the course level) that demonstrate the link of non-formal open learning with formal curriculum and employers' needs.
The OEPass and MicroHE projects, which exploited and sustained valuable outputs from previous relevant projects like the OpenCred study, have developed two valuable tools: a viable foundation for a European credential- documentation mechanism (Learning Passport) and a digital credential-sharing platform (Credential Clearinghouse), which takes into account differences among Europen educational systems.
The e-SLP project's objectives include the formulation of institutional policies, strategies, and frameworks for the development and delivery of flexible, scalable short learning programmes (SLPs) in Europe. It also strives to empower university leadership and staff in the realms of curriculum and course design, quality assurance, and recognition for SLPs that comply with the EQF.
In addition to funding projects like those listed above, the European Commission is also conducting expert consultations and investing great efforts and intelligence into developing its own European framework for digitally signed credentials (to be launched in early 2020).
The Knowledge Innovation Centre has been closely involved in this consultation, bringing to the table results and lessons learned from EU projects and other thematically relevant experience. We hope to continue playing an important role in liaising between the Commission and these transnational collaboration efforts.


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Ealing >
Fishermans Arms
Old Oak Lane, Ealing, London, NW10 6UB
Website	020 8965 8819
Built in 1928 in an area of terraced "workers housing". Now catering to a local Portuguese clientele. No real ale. Football on TV, including Portuguese. Pool. Darts. Table football. Table tennis. Smoking area.
Happening from 14/06/2018 to 15/07/2018 [Expired]
The 2018 World Cup kicks off on Thursday 14th June, and we're all set to welcome you and your friends to enjoy the action. We've got ice cold pitchers of Foster's and Amstel at the ready, so less trips to the bar means more time to watch the match. There really is no better place to…
England v Croatia
It's been a long 28 years in the making, but finally, England have reached the semi-final stages of the World Cup! The Lions will take on Croatia at 7pm on Wednesday, so that's plenty time to get home from work and down the pub for kick-off.
Sweden v England
With barely a moment to recover from Tuesday's historic (not to mention tense) penalty shoot-out victory over Colombia, it's time to do it all over again. Saturday's quarter-final against Sweden kicks-off at 3pm, and unless you have a plane ticket to Russia, the pub is simply the only place…
Willesden Junction (0.21 miles)
Harlesden (0.55 miles)
Le Junction (0.23 miles)
Sportsmans (0.23 miles)
Angies (0.39 miles)
Elm Tree (0.39 miles)
Shawl (0.41 miles)
Pubs & bars in London, NW10
Events in London
Events in NW10
Offers in London
Offers in NW10
News in London
News in NW10
Reviews in London
Reviews in NW10


text:
Rail Heritage »
Kingaroy: Keith Bids Farewell To Railway Memories
Author Topic: Kingaroy: Keith Bids Farewell To Railway Memories (Read 2199 times)
http://southburnett.com.au/news2/2016/04/keith-bids-farewell-to-railway-memories/
Keith Bids Farewell To Railway Memories
by Keith Kratzmann
Almost everyone thinks it was a sad day when the State Government made the final decision to uproot the rail lines in rural parts of south-east Queensland.
However, nobody agrees more than long-term South Burnett resident Keith Bayntun who served some 40 years as an employee of Queensland Rail, progressing from fettler to assistant stationmaster at Wondai and Kingaroy.
Keith and wife Esme have lived in Wondai since 1975 but are now making plans to move closer to Toowoomba for health reasons.
Born at Biggenden, Keith's first job was with the cheese factory at Murgon.
He helped to make mild and matured varieties which were sold in circular blocks ranging from five pounds to a giant 80 pounder.
The factory won national awards for its products over many years. The building still stands at the southern end of Macalister Street, where it's now used by Clovely Estate to produce wines.
Keith's railway career began with concrete construction, working mainly on the section between Murgon and Manyung.
In the earlier 1960s, Keith met and married the former Esme Schafferius.
The couple moved to Garbutt in North Queensland where Keith continued to work on the railways, making sure the lines were safe at night for the long distance passenger trains.
Keith and Esme then moved back to southern Queensland.
He witnessed the beginning of the end of the local rail lines when the Caboolture-Kilcoy line closed in 1964. Then Transport Minister Sir Gordon Chalk was anxious to see an upsurge in road transport.
Years later, Member for Wide Warren Truss – then Shadow Minister for Transport – expressed disgust when the mothballed Kingaroy-Theebine railway line was finally officially closed in 2009.
As Shadow Minister for Transport at the time, Mr Truss slammed former Premier Anna Bligh and her party for announcing the permanent closure of the Theebine-Kingaroy line:
"The Kingaroy line is not now even up for sale as the government has used the cover of the Christmas season to announce its permanent closure," Mr Truss said. "There are already thousands of extra semi-trailers on the road every day because Queensland Rail is no longer even trying to compete for freight business. Queensland Rail now owns more trucks than trains and they fight with motorists for space on an overtaxed road system."
Keith's fettler work took him to Yandina in 1968, where his employment changed to locomotive labour after the emergence of diesel engines.
He took exams and sought a change in position to porter; then he became a night officer at the former station of Netherby near Tiaro.
Keith also did relief work at stations between Gympie and Bundaberg before transferring to the South Burnett as assistant stationmaster at Wondai.
When Wondai closed, he then served five years at Kingaroy until his retirement in 1995.
During his four decades of employment with Queensland railways, Keith witnessed passenger trains, then a combination of passenger and goods carriages followed by the demise of passenger transport to just goods trains.
What We've Lost
Younger South Burnett residents would be unaware of what the total train transport comprised in the region.
There was the main line from Theebine (north of Gympie) to Kingaroy, which opened in 1904.
This was extended to Nanango in 1911 with a steam engine train service each Monday, Wednesday and Friday stopping at sidings along the way which included Edenvale, Hornley, Coolabunia, Hodgleigh and Darlil. This line was closed in 1964.
On Tuesdays and Thursdays, a second branch line service negotiated a rail track to Tarong with stops at Taabinga Village, Boonene, Goodger, Brooklands and Archikoora.
A branch line was also developed from Murgon to Proston via Byee, Windera and Hivesville.
A rail motor service ran between Maryborough and Kingaroy three times weekly from 1929 to 1967.
Throughout World War II, there was also a regular daily rail motor service from Ipswich to Yarraman which carried passengers up until 1997.
There was always lots of discussion about why the railheads at Nanango, Yarraman and Cooyar – which were only 20km apart – were never linked.
It seems ridiculous that Yarraman and Nanango were never connected, which would have provided a circular link from the South Burnett to every major metropolitan city and town in south-east Queensland.
Construction had been earmarked to continue the Brisbane Valley line from Yarraman to Nanango, however thus was interrupted by the outbreak of World War I.
Keith, who knows the rail freight situation better than many of the authorities and parliamentary leaders, says the decision to pull up the rail lines was tragic because so more freight could be carried by rail.
He describes rail as the "forgotten hero" of rural Queensland.
The daily diesel train pulls into Tingoora ... at this time the majority of freight was transported from Brisbane and parts of the northern line to Theebine before proceeding to Wide Bay and the South Burnett (Photo: Queensland Rail)
Memories of rail ... Keith Bayntun at the old Wondai Railway Station (Photo: Keith Kratzmann)
A typical combined goods-passenger train ... when fully loaded with heavy freight, South Burnett trains required two steam engines, particularly on the run up the Kinbombi Range after leaving Kilkivan (Photo: Queensland Rail)
Rail motor services operated from Kingaroy to Maryborough for 38 years until 1967, about the same time that passenger carriages were deleted from goods trains (Photo: Queensland Rail)
A rail motor returned to the South Burnett for one last time in 2004 to take passengers on short trips to mark the centenary of Kingaroy
" He describes rail as the "forgotten hero" of rural Queensland. "
Not forgotten here Keith ...
Footnote: Last regular railmotor to Yarraman was in 1967. The motor to Toogoolawah survived till 93.
I was on the second last train to Yarraman in 1986.
« Last Edit: April 15, 2016, 11:29:56 AM by ozbob »


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« Office 365's nifty new email policy
Your Mac just got a brand new Photos app »
Keep deleted emails forever with Office 365
By Editor | Published: April 30, 2015
Most of us have probably at some point deleted an important email we shouldn't have. It happens. We think an email is pointless and don't want to file it away or create a new folder for it, so instead we carelessly delete it. 30 days pass and then the email is gone for good. And that's when you end up slapping yourself on the forehead wondering why you ever hit the delete button in the first place. The email ended up being important, but now it's too late – you can't get it back. Microsoft Office 365's new policy has now made this problem a thing of the past, allowing deleted emails to be recovered indefinitely.
If you're a regular user of Outlook 365, you're likely aware that you can only recover an email that was deleted 30 days ago or less. After that, it's gone for good. For those that have been agitated by this policy, Office 365 has now made a change that allows emails in the Deleted Items folder to be accessed indefinitely. However, take note that if an end user makes the effort to empty the Deleted Folder, those items will still in fact be unrecoverable.
But what if you don't want to indefinitely recover email?
Believe it or not, indefinite access to emails may come as bad news for some. It can create industry compliance issues for organizations and can also affect offline storage as deleted emails pile up.
Not to fear. Along with this new policy, Office 365 also allows you to customize the retention duration to a time span that works for you. To do this, click on the following:
Office 365 Admin
Exchange Admin Center
Retention Policies
From here you can modify the retention duration of your emails to a time span of your choice.
Want to learn more about this and other cutting-edge Office 365 features? Give us a call today and get all the info you need.
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