Definition:Compact Space/Topology/Subspace/Definition 1

Definition

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

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

The topological subspace $T_H = \struct {H, \tau_H}$ is compact in $T$ if and only if $T_H$ is itself a compact topological space.

Also see

• Equivalence of Definitions of Compact Topological Subspace

• Results about compact spaces can be found here.