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Isolated Points#

Definition: Isolated Point

Let \(X\) be a topological space and let \(S\) be a subset of \(X\).

We say that \(p \in S\) is an isolated point of \(S\) if there is a neighborhood of \(p\) which contains no points of \(S\) other than \(p\):

\[\exists N(p): N(p) \cap S = \{p\}\]