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Regular space

In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These…

Relationships to other separation axioms, Examples and nonexamples & Definitions

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Relationships to other separation axioms

PreregularT21⁄2Completely HausdorffT1Kolmogorov quotients
11 related topics

Examples and nonexamples

Zero-dimensional spaceSmall inductive dimensionBaseClopen setsCounterexamples
10 related topics

Definitions

Closed setPointNeighbourhoodDisjointSeparate
9 related topics

Elementary properties

SubsetLocal baseInteriorsRegular open setsSemiregular
5 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

Definitions

Relationships to other separation axioms

Examples and nonexamples

Elementary properties

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Map overview Semantic statistics

Regular space

Nodes49
Edges48
Triples47
Avg. degree1.96
Density0.040816
Components1

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Regular space

Top relations

related to Relationships to other separation axioms · 14
Regular space → Hausdorff, Hausdorffness, However, In, Kolmogorov, Since, Speaking, T0, T1, T2, T2½, T3, T3-ness, Thus
related to Examples and nonexamples · 9
Regular space → An, As, Every, Hausdorff, Most, Of, On, T0, Tychonoff
related to Definitions · 8
Regular space → Concisely, Hausdorff, Indeed, It, Kolmogorov, T0, T2, T3
related to Elementary properties · 5
Regular space → In, Suppose, Taking, Then, This
completely T2 · 1
Regular space → (completely Hausdorff)
T0 · 1
Regular space → (Kolmogorov)
T1 · 1
Regular space → (Fréchet)
T2 · 1
Regular space → (Hausdorff)
T2½ · 1
Regular space → (Urysohn)
T3 · 1
Regular space → (regular Hausdorff)

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Important terminology

regular space hausdorff spaces t3 topological point t0 regularity thus condition usually preregular base completely closed open also every neighborhoods

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Regular spacecompletely T2(completely Hausdorff)1.00infobox
Regular spaceT0(Kolmogorov)1.00infobox
Regular spaceT1(Fréchet)1.00infobox
Regular spaceT2(Hausdorff)1.00infobox
Regular spaceT2½(Urysohn)1.00infobox
Regular spaceT3(regular Hausdorff)1.00infobox
Regular spaceT3½(Tychonoff)1.00infobox
Regular spaceT4(normal Hausdorff)1.00infobox
Regular spaceT5(completely normal Hausdorff)1.00infobox
Regular spaceT6(perfectly normal Hausdorff)1.00infobox
Regular spaceis atopological space where every point has an open neighbourhood that is regular0.90text
Regular spacerelated to DefinitionsConcisely0.60section

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