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Normal space

In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A normal Hausdorff space is called a T4 space. Strengthenings of these concepts are detailed in the article below and include completely normal spaces…

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completely T2
(completely Hausdorff)
T0
(Kolmogorov)
T1
(Fréchet)
T2
(Hausdorff)
T2½
(Urysohn)
T3
(regular Hausdorff)

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Overview

Definitions

Examples of normal spaces

Examples of non-normal spaces

Properties

Relationships to other separation axioms

Advanced semantic analysis

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Map overview Semantic statistics

Normal space

Nodes77
Edges76
Triples38
Avg. degree1.97
Density0.025974
Components1

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Normal space

Top relations

related to Relationships to other separation axioms · 9
Normal space → Every, Hausdorff, If, R0, T1, Taking Kolmogorov, These, Thus, Tychonoff
related to Related definitions · 6
Normal space → Also, Hausdorff, It, T1, T4, T5
related to Examples of non-normal spaces · 4
Normal space → An, Arthur Harold Stone, More, Zariski
is a · 3
Normal space → topological space in which any two disjoint closed sets have disjoint open neighborhoods, topological space where every point has an open neighbourhood that is normal, topological space X
related to Definitions · 2
Normal space → Intuitively, The
related to Properties · 2
Normal space → Every, The
see also · 2
Normal space → Collectionwise, Property
completely T2 · 1
Normal space → (completely Hausdorff)
T0 · 1
Normal space → (Kolmogorov)
T1 · 1
Normal space → (Fréchet)

Important terminology Word statistics

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Important terminology

normal space hausdorff spaces completely closed every topological t4 disjoint sets regular topology perfectly open tychonoff continuous product isbn also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Normal spacecompletely T2(completely Hausdorff)1.00infobox
Normal spaceT0(Kolmogorov)1.00infobox
Normal spaceT1(Fréchet)1.00infobox
Normal spaceT2(Hausdorff)1.00infobox
Normal spaceT2½(Urysohn)1.00infobox
Normal spaceT3(regular Hausdorff)1.00infobox
Normal spaceT3½(Tychonoff)1.00infobox
Normal spaceT4(normal Hausdorff)1.00infobox
Normal spaceT5(completely normal Hausdorff)1.00infobox
Normal spaceT6(perfectly normal Hausdorff)1.00infobox
Normal spaceis atopological space in which any two disjoint closed sets have disjoint open neighborhoods0.90text
Normal spaceis atopological space X0.90text
Normal spaceis atopological space where every point has an open neighbourhood that is normal0.90text

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