Definition:Closed Set

{{about|closed sets in the context of Topology (including its application to Metric Spaces, Complex Analysis and Real Analysis}|Definition:Closed}}

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

Let $H \subseteq S$.

Metric Space
In the context of metric spaces, the same definition applies:

Under Closure Operator
The concept of closure can be made more generally than on a topological space:

Also see

 * Definition:Closed Mapping
 * Definition:Regular Closed Set