# countably compact

A topological space $X$ is said to be countably compact if every countable open cover has a finite subcover.

Countable compactness is equivalent to limit point compactness if $A$ is $T_{1}$ spaces, and is equivalent to compactness (http://planetmath.org/Compact) if $X$ is a metric space.

Title countably compact CountablyCompact 2013-03-22 12:06:43 2013-03-22 12:06:43 Evandar (27) Evandar (27) 8 Evandar (27) Definition msc 54D20 countable compactness Compact Lindelof LimitPointCompact