# Definition:Isolated Point (Topology)/Space

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## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

$x \in S$ is an **isolated point of $T$** if and only if:

- $\exists U \in \tau: U = \left\{{x}\right\}$

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

## Also see

- Results about
**isolated points**can be found here.