Difference between revisions of "Compactness"
From Encyclopedia of Mathematics
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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. | 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. | ||
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Revision as of 20:59, 2 November 2014
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 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=25122
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=25122
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