# Definition:Countably Compact Space/Definition 2

## Definition

A topological space $T = \left({S, \tau}\right)$ is countably compact if and only if:

every countable set of closed sets of $T$ whose intersection is empty has a finite subset whose intersection is empty.

That is, $T$ satisfies the countable finite intersection axiom.

## Also see

• Results about countably compact spaces can be found here.