: Mathématiques: isolated point

geometry > topological space > isolated point

isolated point

In mathematics, a point $x$ is called an isolated point of a subset $S$ (in a topological space $X$ ) if $x$ is an element of $S$ and there exists a neighborhood of $x$ that does not contain any other points of $S$ . This is equivalent to saying that the singleton ${x}$ is an open set in the topological space $S$ (considered as a subspace of $X$ ). Another equivalent formulation is: an element $x$ of $S$ is an isolated point of $S$ if and only if it is not a limit point of $S$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Isolated_point)

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