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Hausdorff space

In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), T2 space or separated space, is a topological space where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used…

Examples of Hausdorff and non-Hausdorff spaces, Properties & Definitions

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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

Equivalences

Examples of Hausdorff and non-Hausdorff spaces

Properties

Preregularity versus regularity

Variants

Algebra of functions

Academic humour

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Hausdorff space

Nodes100
Edges99
Triples95
Avg. degree1.98
Density0.02
Components1

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Hausdorff space

Top relations

related to References · 24
Hausdorff space → Academic Press, Addison-Wesley, Analysis, Arkhangelskii, Bourbaki, CA, Dover Publications, Elements, EMS Press, Encyclopedia, Eric, General Topology, Handbook, Hausdorff, ISBN, Its Foundations, Mathematics, OCLC, Pontryagin, San Diego
related to Academic humour · 10
Hausdorff space → Bonn, Felix Hausdorff, German, Hausdorff, Hausdorff-Raum, In, Mathematics Institute, Raum, This, University
related to Preregularity versus regularity · 9
Hausdorff space → All, Although Hausdorff, Hausdorff, However, Most, On, Such, There, Thus
related to Definitions · 8
Hausdorff space → Hausdorff, Points, R1, T0, T1, T2, The, This
related to Properties · 8
Hausdorff space → Every Hausdorff, Hausdorff, In, R0, Similarly, Sober, Subspaces, T1
see also · 8
Hausdorff space → Axioms, Fixed-point, Function, Generalization, Hausdorff, Locally Hausdorff, Space, Weak Hausdorff
related to Equivalences · 6
Hausdorff space → Any, Delta, For, Hausdorff, Limits, The
related to Algebra of functions · 5
Hausdorff space → Banach, Hausdorff, Stone, The, This
related to Examples of Hausdorff and non-Hausdorff spaces · 5
Hausdorff space → Almost, Hausdorff, In, More, T1
is a · 2
Hausdorff space → commutative C, Sober space although the converse is in general not true.Another property of Hausdorff spaces is that each compact set is a closed set

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Important terminology

hausdorff space spaces displaystyle closed topological preregular compact topology set points also separated open continuous condition every regular nets neighbourhoods

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hausdorff spacecompletely T2(completely Hausdorff)1.00infobox
Hausdorff spaceT0(Kolmogorov)1.00infobox
Hausdorff spaceT1(Fréchet)1.00infobox
Hausdorff spaceT2(Hausdorff)1.00infobox
Hausdorff spaceT2½(Urysohn)1.00infobox
Hausdorff spaceT3(regular Hausdorff)1.00infobox
Hausdorff spaceT3½(Tychonoff)1.00infobox
Hausdorff spaceT4(normal Hausdorff)1.00infobox
Hausdorff spaceT5(completely normal Hausdorff)1.00infobox
Hausdorff spaceT6(perfectly normal Hausdorff)1.00infobox
Hausdorff spaceis aSober space although the converse is in general not true.Another property of Hausdorff spaces is that each compact set is a closed set0.90text
Hausdorff spaceis acommutative C0.90text

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