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Tychonoff space

In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space is any completely regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff).

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

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Tychonoff space

Nodes76
Edges75
Triples50
Avg. degree1.97
Density0.026316
Components1

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Tychonoff space

Top relations

related to Examples · 13
Tychonoff space → Almost, But, Euclidean, Every, Every CW, For, Generalizing, Hausdorff, In, Other, The, The Niemytzki, Tychonoff
related to Compactifications · 8
Tychonoff space → Among, Given, Hausdorff, In, It, Of, Stone, Tychonoff
related to Definitions · 7
Tychonoff space → Equivalently, Hausdorff, In, T3, T3½, Tychonoff, Tπ
related to Embeddings · 7
Tychonoff space → Every Tychonoff, Hausdorff, In, More, Since, Tychonoff, Tychonoff's
related to Preservation · 5
Tychonoff space → Complete, Every, It, Specifically, Tychonoff
completely T2 · 1
Tychonoff space → (completely Hausdorff)
T0 · 1
Tychonoff space → (Kolmogorov)
T1 · 1
Tychonoff space → (Fréchet)
T2 · 1
Tychonoff space → (Hausdorff)
T2½ · 1
Tychonoff space → (Urysohn)

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Important terminology

regular tychonoff completely space displaystyle hausdorff every spaces topological topology one continuous real-valued compact also uniform closed tau examples quotients

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tychonoff spacecompletely T2(completely Hausdorff)1.00infobox
Tychonoff spaceT0(Kolmogorov)1.00infobox
Tychonoff spaceT1(Fréchet)1.00infobox
Tychonoff spaceT2(Hausdorff)1.00infobox
Tychonoff spaceT2½(Urysohn)1.00infobox
Tychonoff spaceT3(regular Hausdorff)1.00infobox
Tychonoff spaceT3½(Tychonoff)1.00infobox
Tychonoff spaceT4(normal Hausdorff)1.00infobox
Tychonoff spaceT5(completely normal Hausdorff)1.00infobox
Tychonoff spaceT6(perfectly normal Hausdorff)1.00infobox
Tychonoff spacerelated to CompactificationsOf0.60section
Tychonoff spacerelated to CompactificationsHausdorff0.60section

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