# Definition:Isolated Point (Topology)/Subset

## Definition

### Definition 1

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

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

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

### Definition 2

$x \in H$ is an isolated point of $H$ if and only if $x$ is not a limit point of $H$.

That is, if and only if $x$ is not in the derived set of $H$.

## Also see

• Results about isolated points can be found here.