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单词 LindelofSpace
释义

Lindelöf space


Definition

A topological spaceMathworldPlanetmath is said to be Lindelöf if every open cover has a countableMathworldPlanetmath subcover.

Notes

A second-countable space is Lindelöf.A compact space is Lindelöf.

A regularPlanetmathPlanetmathPlanetmathPlanetmath (http://planetmath.org/T3Space) Lindelöf space is http://planetmath.org/node/1530normal.

Fσ sets (http://planetmath.org/F_sigmaSet) in Lindelöf spaces are Lindelöf.ContinuousPlanetmathPlanetmath images of Lindelöf spaces are Lindelöf.

A Lindelöf space is compactPlanetmathPlanetmath if and only if it is countably compact.

TitleLindelöf space
Canonical nameLindelofSpace
Date of creation2013-03-22 12:06:34
Last modified on2013-03-22 12:06:34
Owneryark (2760)
Last modified byyark (2760)
Numerical id11
Authoryark (2760)
Entry typeDefinition
Classificationmsc 54D20
Related topicSecondCountable
Related topicSeparablePlanetmathPlanetmath
Related topicCompact
Related topicLindelofTheorem
Related topicCompactMetricSpacesAreSecondCountable
Related topicErnstLindelof
DefinesLindelöf
DefinesLindelöf property
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更新时间:2025/5/4 20:28:40