Definition:Isolated Point (Topology)/Subset/Definition 1

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Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a subset of $S$.

$x \in H$ is an isolated point of $H$ if and only if:

$\exists U \in \tau: U \cap H = \set x$

That is, if and only if there exists an open set of $T$ containing no points of $H$ other than $x$.

Also see

  • Results about isolated points can be found here.