\begin{definition}[Definition:Closed Neighborhood]
Let $\struct {S, \tau}$ be a topological space.
Let $A \subseteq S$ be a subset of $S$.
Let $N_A$ be a neighborhood of $A$.
If $\relcomp S {N_A} \in \tau$, that is if $N_A$ is closed in $S$, then $N_A$ is called a '''closed neighborhood'''.
\end{definition}