|Jan30-13, 08:44 AM||#1| Continuous functions on metric space, M
If every continuous function on M is bounded, what does this
mean? I am not sure what this function actually is... is it a
mapping from M -> M or some other mapping? Is the image of the
function in M? Any help would be greatly appreciated! |Jan30-13,
11:33 AM||#2| |Jan30-13, 11:38 AM||#3| A map
[itex]f:X\rightarrow M[/itex] where X is a set and M is a metric
space, is called bounded if the image f(X) is bounded. This
means that there is an [itex]x\in X[/itex] and an
[itex]\varepsilon>0[/itex] such that [itex]f(X)\subseteq
B(f(x),\varepsilon)[/itex]. This is what I would call bounded.
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