Definition:Sigma-Compact Space

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

$T$ is $\sigma$-compact $S$ is the union of the underlying sets of countably many compact subspaces of $T$.

This can be expressed more efficiently as:

$T$ is $\sigma$-compact it is the union of countably many compact subspaces.

Also known as
A $\sigma$-compact space is also known as a space that is countable at infinity.

Also see

 * Definition:$\sigma$-Locally Compact Space
 * Definition:Weakly $\sigma$-Locally Compact Space