\begin{definition}[Definition:Closed under Mapping]
Let $f: S \to T$ be a mapping.
Let $S' \subseteq S$.
Then $S'$ is '''closed under $f$''' {{iff}}:
:$f \sqbrk {S'} \subseteq S'$
where $f \sqbrk {S'}$ is the image of $S'$ under $f$.
That is:
:$x \in S' \implies \map f x \in S'$
\end{definition}