PlanetMath: countably compact

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countably compact

(Definition)

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 if $X$ is a metric space.

"countably compact" is owned by Evandar.

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Other names:

countable compactness

Keywords:

topology

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Cross-references: metric space, limit point compactness, equivalent, subcover, finite, open cover, countable, topological space
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This is version 4 of countably compact, born on 2002-01-04, modified 2002-02-03.
Object id is 1233, canonical name is CountablyCompact.
Accessed 5882 times total.

Classification:

54D20 (General topology :: Fairly general properties :: Noncompact covering properties )

Pending Errata and Addenda

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