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

Then $H$ is compact the corresponding subspace is a compact subspace.

Also see

 * Equivalent Definitions of Compactness


 * Definition:Hereditarily Compact