# Definition:Compact Space/Topology/Subspace/Definition 2

## Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a subset of $S$.

$H$ is compact in $T$ if and only if every open cover $\CC \subseteq \tau$ for $H$ has a finite subcover.

## Also see

• Results about compact spaces can be found here.