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Paracompact space

In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions of unity subordinate…

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Definition

Examples

Properties

Paracompact Hausdorff spaces

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Paracompact space

Nodes86
Edges85
Triples24
Avg. degree1.98
Density0.023256
Components1

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Paracompact space

Top relations

related to Properties · 10
Paracompact space → Banach, F-sigma, Hausdorff, In, Lindelöf, Michael, Michael's, Paracompactness, Smirnov, This
related to Paracompact Hausdorff spaces · 6
Paracompact space → Every, Hausdorff, Jean Dieudonné, On, Paracompact, Theorem
related to External links · 4
Paracompact space → EMS Press, Encyclopedia, Mathematics, Paracompact
related to Comparison of properties with compactness · 3
Paracompact space → Every, Hausdorff, Paracompactness
is a · 1
Paracompact space → topological space in which every open cover has an open refinement that is locally finite

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Important terminology

paracompact space every hausdorff cover open spaces compact locally product refinement topological normal finite set displaystyle topology theorem unity closed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Paracompact spaceis atopological space in which every open cover has an open refinement that is locally finite0.90text
Paracompact spacerelated to Comparison of properties with compactnessParacompactness0.60section
Paracompact spacerelated to Comparison of properties with compactnessEvery0.60section
Paracompact spacerelated to Comparison of properties with compactnessHausdorff0.60section
Paracompact spacerelated to External linksParacompact0.60section
Paracompact spacerelated to External linksEncyclopedia0.60section
Paracompact spacerelated to External linksMathematics0.60section
Paracompact spacerelated to External linksEMS Press0.60section
Paracompact spacerelated to Paracompact Hausdorff spacesParacompact0.60section
Paracompact spacerelated to Paracompact Hausdorff spacesHausdorff0.60section
Paracompact spacerelated to Paracompact Hausdorff spacesTheorem0.60section
Paracompact spacerelated to Paracompact Hausdorff spacesJean Dieudonné0.60section

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    Min side: 3
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