Definition:Compact Space/Topology

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

Then $T$ is compact every open cover for $S$ has a finite subcover.

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

Also see

 * Equivalent Definitions of Compactness


 * Definition:Hereditarily Compact Space