# Compactness

From Encyclopedia of Mathematics

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).

#### 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.

**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