Definition:Deleted Neighborhood/Topology

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $x \in S$.

Let $V \subseteq S$ be a neighborhood of $x$.

Then $V \setminus \left\{{x}\right\}$ is called a deleted neighborhood of $x$.

That is, it is a neighborhood of $x$ with $x$ itself removed.