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