\begin{definition}[Definition:Included Set Topology]
Let $S$ be a set which is non-null.
Let $H \subseteq S$ be some subset of $S$.
We define a subset $\tau_H$ of the power set $\powerset S$ as:
:$\tau_H = \set {A \subseteq S: H \subseteq A} \cup \set \O$
that is, all the subsets of $S$ which are supersets of $H$, along with the empty set $\O$.
Then $\tau_H$ is a topology called the '''included set topology on $S$ by $H$''', or just '''an included set topology'''.
The topological space $T = \struct {S, \tau_H}$ is called the '''included set space on $S$ by $H$''', or just '''an included set space'''.
\end{definition}