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Weak Hausdorff space

In mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space into the space is closed. The notion was introduced by M. C. McCord to remedy an inconvenience of working with the category of Hausdorff spaces. It is often used in tandem with compactly generated…

Overview, K-Hausdorff spaces & Δ-Hausdorff spaces

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Overview

13 related topics

K-Hausdorff spaces

2 related topics

Δ-Hausdorff spaces

1 related topics

Key facts & relationships

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

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Overview

K-Hausdorff spaces

Δ-Hausdorff spaces

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Map overview Semantic statistics

Weak Hausdorff space

Nodes20
Edges19
Triples14
Avg. degree1.9
Density0.1
Components1

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Weak Hausdorff space

Top relations

related to Δ-Hausdorff spaces · 4
Weak Hausdorff space → Delta, Every, Hausdorff, T1
completely T2 · 1
Weak Hausdorff space → (completely Hausdorff)
T0 · 1
Weak Hausdorff space → (Kolmogorov)
T1 · 1
Weak Hausdorff space → (Fréchet)
T2 · 1
Weak Hausdorff space → (Hausdorff)
T2½ · 1
Weak Hausdorff space → (Urysohn)
T3 · 1
Weak Hausdorff space → (regular Hausdorff)
T3½ · 1
Weak Hausdorff space → (Tychonoff)
T4 · 1
Weak Hausdorff space → (normal Hausdorff)
T5 · 1
Weak Hausdorff space → (completely normal Hausdorff)

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Important terminology

hausdorff space closed compact every displaystyle weak k-hausdorff spaces continuous topological image kc subspace map k-closed subseteq topology subset compactly

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Weak Hausdorff spacecompletely T2(completely Hausdorff)1.00infobox
Weak Hausdorff spaceT0(Kolmogorov)1.00infobox
Weak Hausdorff spaceT1(Fréchet)1.00infobox
Weak Hausdorff spaceT2(Hausdorff)1.00infobox
Weak Hausdorff spaceT2½(Urysohn)1.00infobox
Weak Hausdorff spaceT3(regular Hausdorff)1.00infobox
Weak Hausdorff spaceT3½(Tychonoff)1.00infobox
Weak Hausdorff spaceT4(normal Hausdorff)1.00infobox
Weak Hausdorff spaceT5(completely normal Hausdorff)1.00infobox
Weak Hausdorff spaceT6(perfectly normal Hausdorff)1.00infobox
Weak Hausdorff spacerelated to Δ-Hausdorff spacesHausdorff0.60section
Weak Hausdorff spacerelated to Δ-Hausdorff spacesEvery0.60section

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