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. Bourbaki uses the term "compact" to include Hausdorff, and more generally uses the term "quasi-compact". |
For references, see [[Compact space]]. | For references, see [[Compact space]]. | ||
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| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> Nicolas Bourbaki, "General Topology: Chapters 1-4", Springer (1998) ISBN 3-540-64241-2</TD></TR> | ||
| + | </table> | ||
[[Category:Topology]] | [[Category:Topology]] | ||
Revision as of 21:08, 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. Bourbaki uses the term "compact" to include Hausdorff, and more generally uses the term "quasi-compact".
For references, see Compact space.
References
| [a1] | Nicolas Bourbaki, "General Topology: Chapters 1-4", Springer (1998) ISBN 3-540-64241-2 |
How to Cite This Entry:
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=34255
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=34255
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