# Definition:Closed Set/Topology/Definition 1

## Definition

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

Let $H \subseteq S$.

$H$ is closed (in $T$) if and only if its complement $S \setminus H$ is open in $T$.

That is, $H$ is closed if and only if $\left({S \setminus H}\right) \in \tau$.

That is, if and only if $S \setminus H$ is an element of the topology of $T$.

## Also see

• Results about closed sets can be found here.