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normal


A topological spaceMathworldPlanetmath X is said to be normal if X is T1 (i.e. singletons are closed), and for all disjoint closed sets D,FX there exist disjoint open sets U and V such that CU and DV (i.e, X is also T4).

Some authors do not require the T1 axiom as part of this definition.

Titlenormal
Canonical nameNormal
Date of creation2013-03-22 12:12:39
Last modified on2013-03-22 12:12:39
OwnerKoro (127)
Last modified byKoro (127)
Numerical id14
AuthorKoro (127)
Entry typeDefinition
Classificationmsc 54D15
SynonymnormalityPlanetmathPlanetmath
Synonymnormal
Related topicSeparationAxioms
Related topicTychonoffPlanetmathPlanetmath
Related topicHausdorffPlanetmathPlanetmath
Related topicCompletelyNormal
Related topicT2Space
Related topicAConnectedNormalSpaceWithMoreThanOnePointIsUncountable2
Related topicAConnectedNormalSpaceWithMoreThanOnePointIsUncountable
Related topicApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces
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更新时间:2025/5/4 11:31:06