Definition:Countably Compact Space/Definition 2

Definition

A topological space $T = \struct {S, \tau}$ 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

• Equivalence of Definitions of Countably Compact Space

• Results about countably compact spaces can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Global Compactness Properties: $\text {CC}_4$