countably compact

A topological spaceMathworldPlanetmath X is said to be countably compact if every countableMathworldPlanetmath open cover has a finite subcover.

Countable compactness is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to limit point compactness if A is T1 spaces, and is equivalent to compactness ( 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