Definition:Deleted Neighborhood/Topology
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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.