Category:Definitions/Closed Sets

This category contains definitions related to Closed Sets in the context of Topology.
Related results can be found in Category:Closed Sets.

$H$ 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 $T$.