\begin{definition}[Definition:Neighborhood (Topology)/Point]
Let $T = \struct {S, \tau}$ be a topological space.
Let $z \in S$ be a point in a $S$.
Let $N_z$ be a subset of $S$ which contains (as a subset) an open set of $T$ which itself contains (as an element) $z$.
Then $N_z$ is a '''neighborhood''' of $z$.
That is:
:$\exists U \in \tau: z \in U \subseteq N_z \subseteq S$
\end{definition}