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Difference between revisions of "Compactness"

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A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering. The term  "bicompactness"  is also used instead of  "compactness"  (in Russian). Topological spaces with the compactness property are called compact spaces (cf. [[Compact space|Compact space]]).
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A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering. Topological spaces with the compactness property are called [[Compact space|compact spaces. In Russian literature, "compactness" is often used for the notion of countable compactness, and "bicompactness" for general compactness.
 
 
 
 
====Comments====
 
"Compactness" in the Russian literature often refers to the notion of countable compactness"Bicompactness"  in the Russian literature being the Western notion of  "compactness" .
 
  
 
For references, see [[Compact space|Compact space]].
 
For references, see [[Compact space|Compact space]].

Revision as of 06:35, 23 April 2012

A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering. Topological spaces with the compactness property are called [[Compact space|compact spaces. In Russian literature, "compactness" is often used for the notion of countable compactness, and "bicompactness" for general compactness.

For references, see Compact space.

How to Cite This Entry:
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=11573
This article was adapted from an original article by A.V. Arkhangel'skii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article