Definition:Countably Compact Space/Definition 2

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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.