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Collectionwise normal space

In mathematics, a topological space X {\displaystyle X} is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X {\displaystyle X} there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. Here a family F {\displaystyle {\mathcal {F}}} of subsets of X {\displaystyle X} is called discrete…

Properties, Hereditarily collectionwise normal space & Overview

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Properties

Hereditarily collectionwise normal space

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Collectionwise normal space

Nodes27
Edges26
Triples13
Avg. degree1.93
Density0.074074
Components1

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Collectionwise normal space

Top relations

related to Properties · 11
Collectionwise normal space → An Fσ-set, Every, Hausdorff, In, Moore, Note, Proof, T1, The, The Hausdorff, Use
related to Hereditarily collectionwise normal space · 2
Collectionwise normal space → In, The

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Important terminology

normal collectionwise space every family subsets displaystyle discrete called sets metrizable pairwise disjoint hereditarily topology topological open equivalent ui definition

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SubjectPredicateObjectConfidenceSrc
Collectionwise normal spacerelated to Hereditarily collectionwise normal spaceIn0.60section
Collectionwise normal spacerelated to Hereditarily collectionwise normal spaceThe0.60section
Collectionwise normal spacerelated to PropertiesHausdorff0.60section
Collectionwise normal spacerelated to PropertiesIn0.60section
Collectionwise normal spacerelated to PropertiesNote0.60section
Collectionwise normal spacerelated to PropertiesThe Hausdorff0.60section
Collectionwise normal spacerelated to PropertiesT10.60section
Collectionwise normal spacerelated to PropertiesEvery0.60section
Collectionwise normal spacerelated to PropertiesProof0.60section
Collectionwise normal spacerelated to PropertiesUse0.60section
Collectionwise normal spacerelated to PropertiesAn Fσ-set0.60section
Collectionwise normal spacerelated to PropertiesThe0.60section

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