Isolated point

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This article is about a basic definition in topology.
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Definition

A point in a topological space is said to be an isolated point if the singleton set comprising that point, is an open subset.

Often, we talk of isolated points in a subset of a topological space. An isolated point in a subset is simply an isolated point in the above sense, with respect to the subset endowed with the subspace topology. Equivalently, the point is in the subset but is not a limit point of the subset.