Definition:Deleted Neighborhood/Topology

Definition

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.

Also known as

A deleted neighborhood is also called a punctured neighborhood.