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
Canonical name	CountablyCompact
Date of creation	2013-03-22 12:06:43
Last modified on	2013-03-22 12:06:43
Owner	Evandar (27)
Last modified by	Evandar (27)
Numerical id	8
Author	Evandar (27)
Entry type	Definition
Classification	msc 54D20
Synonym	countable compactness
Related topic	Compact
Related topic	Lindelof
Related topic	LimitPointCompact