\begin{definition}[Definition:Open Neighborhood]
Let $T = \struct {S, \tau}$ be a topological space.
Let $A \subseteq S$ be a subset of $S$.
Let $N_A$ be a neighborhood of $A$.
Let:
:$N_A \in \tau$
That is, let $N_A$ itself be an open set of $T$.
Then $N_A$ is called an '''open neighborhood of $A$ in $T$'''.
\end{definition}