\begin{definition}[Definition:Deleted Neighborhood/Topology]
Let $T = \struct {S, \tau}$ be a topological space.
Let $x \in S$.
Let $V \subseteq S$ be a neighborhood of $x$.
Then $V \setminus \set x$ is called a '''deleted neighborhood of $x$'''.
That is, it is a neighborhood of $x$ with $x$ itself ''removed''.
\end{definition}