Difference between revisions of "Completeness (in topology)"
From Encyclopedia of Mathematics
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| − | A property of a space requiring that sequences, directions or families of sets, satisfying the Cauchy condition or generalizations of it converge. (See [[Complete space|Complete space]] and [[Cauchy criteria]].) | + | {{MSC|54-XX}} |
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| + | A property of a space requiring that sequences, directions or families of sets, satisfying the [[Cauchy sequence|Cauchy condition]] (or appropriate generalizations of it, see [[Cauchy filter]]) converge. (See also [[Complete metric space]], [[Complete uniform space]], [[Complete space|Complete space]], [[Completion]], and [[Cauchy criteria]].) | ||
Latest revision as of 22:07, 12 December 2015
2020 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://encyclopediaofmath.org/index.php?title=Completeness_(in_topology)&oldid=30856
Completeness (in topology). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Completeness_(in_topology)&oldid=30856
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