Definition:Countably Compact Space/Definition 2

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

 * Equivalence of Definitions of Countably Compact Space