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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).


"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.

How to Cite This Entry:
Compactness. Encyclopedia of Mathematics. URL:
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