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- Orthocompact_space abstract "In mathematics, in the field of general topology, a topological space is said to be orthocompact if every open cover has an interior preserving open refinement. That is, given an open cover of the topological space, there is a refinement which is also an open cover, with the further property that at any point, the intersection of all open sets in the refinement containing that point, is also open.If the number of open sets containing the point is finite, then their intersection is clearly open. That is, every point finite open cover is interior preserving. Hence, we have the following: every metacompact space, and in particular, every paracompact space, is orthocompact.Useful theorems: Orthocompactness is a topological invariant; that is, it is preserved by homeomorphisms. Every closed subspace of an orthocompact space is orthocompact. A topological space X is orthocompact if and only if every open cover of X by basic open subsets of X has an interior-preserving refinement that is an open cover of X. The product X × [0,1] of the closed unit interval with an orthocompact space X is orthocompact if and only if X is countably metacompact. (B.M. Scott) Every orthocompact space is countably orthocompact. Every countably orthocompact Lindelöf space is orthocompact.↑".
- Orthocompact_space wikiPageID "5074937".
- Orthocompact_space wikiPageRevisionID "544373090".
- Orthocompact_space hasPhotoCollection Orthocompact_space.
- Orthocompact_space subject Category:Compactness_(mathematics).
- Orthocompact_space subject Category:Properties_of_topological_spaces.
- Orthocompact_space type Abstraction100002137.
- Orthocompact_space type Possession100032613.
- Orthocompact_space type PropertiesOfTopologicalSpaces.
- Orthocompact_space type Property113244109.
- Orthocompact_space type Relation100031921.
- Orthocompact_space comment "In mathematics, in the field of general topology, a topological space is said to be orthocompact if every open cover has an interior preserving open refinement. That is, given an open cover of the topological space, there is a refinement which is also an open cover, with the further property that at any point, the intersection of all open sets in the refinement containing that point, is also open.If the number of open sets containing the point is finite, then their intersection is clearly open.".
- Orthocompact_space label "Orthocompact space".
- Orthocompact_space sameAs 직교_콤팩트_공간.
- Orthocompact_space sameAs m.0d1kvn.
- Orthocompact_space sameAs Q7104431.
- Orthocompact_space sameAs Q7104431.
- Orthocompact_space sameAs Orthocompact_space.
- Orthocompact_space wasDerivedFrom Orthocompact_space?oldid=544373090.
- Orthocompact_space isPrimaryTopicOf Orthocompact_space.