Namespaces
Variants
Actions

Compactness

From Encyclopedia of Mathematics
Revision as of 06:35, 23 April 2012 by TBloom (talk | contribs) (Added TeX done tag; rewrite for clarity.)
Jump to: navigation, search

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