Definition:Closed Set/Topology/Definition 1

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Let $T = \struct {S, \tau}$ 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 $\paren {S \setminus H} \in \tau$.

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.