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- Paracompact_space abstract "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 to any open cover. Paracompact spaces are sometimes required to also be Hausdorff.Every closed subspace of a paracompact space is paracompact. While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets. A space such that every subspace of it is a paracompact space is called hereditarily paracompact. This is equivalent to requiring that every open subspace be paracompact.Tychonoff's theorem (which states that the product of any collection of compact topological spaces is compact) does not generalize to paracompact spaces in that the product of paracompact spaces need not be paracompact. However, the product of a paracompact space and a compact space is always paracompact.Every metric space is paracompact. A topological space is metrizable if and only if it is a paracompact and locally metrizable Hausdorff space.".
- Paracompact_space wikiPageExternalLink paracompactness.
- Paracompact_space wikiPageID "48631".
- Paracompact_space wikiPageRevisionID "605961403".
- Paracompact_space hasPhotoCollection Paracompact_space.
- Paracompact_space id "p/p071300".
- Paracompact_space title "Paracompact space".
- Paracompact_space subject Category:Compactness_(mathematics).
- Paracompact_space subject Category:Properties_of_topological_spaces.
- Paracompact_space subject Category:Separation_axioms.
- Paracompact_space type Abstraction100002137.
- Paracompact_space type AuditoryCommunication107109019.
- Paracompact_space type Communication100033020.
- Paracompact_space type Maxim107152948.
- Paracompact_space type Possession100032613.
- Paracompact_space type PropertiesOfTopologicalSpaces.
- Paracompact_space type Property113244109.
- Paracompact_space type Relation100031921.
- Paracompact_space type Saying107151380.
- Paracompact_space type SeparationAxioms.
- Paracompact_space type Speech107109196.
- Paracompact_space comment "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 to any open cover. Paracompact spaces are sometimes required to also be Hausdorff.Every closed subspace of a paracompact space is paracompact.".
- Paracompact_space label "Espace paracompact".
- Paracompact_space label "Espacio paracompacto".
- Paracompact_space label "Espaço paracompacto".
- Paracompact_space label "Paracompact space".
- Paracompact_space label "Paracompacte ruimte".
- Paracompact_space label "Parakompakter Raum".
- Paracompact_space label "Przestrzeń parazwarta".
- Paracompact_space label "Spazio paracompatto".
- Paracompact_space label "Паракомпактное пространство".
- Paracompact_space label "仿紧空间".
- Paracompact_space sameAs Parakompakter_Raum.
- Paracompact_space sameAs Espacio_paracompacto.
- Paracompact_space sameAs Espace_paracompact.
- Paracompact_space sameAs Spazio_paracompatto.
- Paracompact_space sameAs 파라콤팩트_공간.
- Paracompact_space sameAs Paracompacte_ruimte.
- Paracompact_space sameAs Przestrzeń_parazwarta.
- Paracompact_space sameAs Espaço_paracompacto.
- Paracompact_space sameAs m.0c_qx.
- Paracompact_space sameAs Q970119.
- Paracompact_space sameAs Q970119.
- Paracompact_space sameAs Paracompact_space.
- Paracompact_space wasDerivedFrom Paracompact_space?oldid=605961403.
- Paracompact_space isPrimaryTopicOf Paracompact_space.