# Completeness (in topology)

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 54-XX [MSN][ZBL]

A property of a space requiring that sequences, directions or families of sets, satisfying the Cauchy condition (or appropriate generalizations of it, see Cauchy filter) converge. (See also Complete metric space, Complete uniform space, Complete space, Completion, and Cauchy criteria.)

**How to Cite This Entry:**

Completeness (in topology).

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Completeness_(in_topology)&oldid=36902

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