# Definition:Isolated Point (Topology)/Space

## 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.