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单词 T1Space
释义

T1 space


A topological spaceMathworldPlanetmath (X,τ) is said to be T1 (or said to hold the T1 axiom) if for all distinct points x,yX (xy), there exists an open set Uτ such that xU and yU.

A space being T1 is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to the following statements:

  • For every xX, the set {x} is closed.

  • Every subset of X is equal to the intersectionMathworldPlanetmath of all the open sets that contain it.

  • Distinct points are separated.

TitleT1 space
Canonical nameT1Space
Date of creation2013-03-22 12:18:14
Last modified on2013-03-22 12:18:14
Ownerdrini (3)
Last modified bydrini (3)
Numerical id10
Authordrini (3)
Entry typeDefinition
Classificationmsc 54D10
SynonymT1
Related topicT0Space
Related topicT2Space
Related topicT3Space
Related topicRegularSpace
Related topicASpaceIsT1IfAndOnlyIfEverySubsetAIsTheIntersectionOfAllOpenSetsContainingA
Related topicSierpinskiSpace
Related topicPropertyThatCompactSetsInASpaceAreClosedLiesStrictlyBetweenT1AndT2
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更新时间:2025/5/4 14:36:10