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Kolmogorov space

In topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of X, at least one of them has a neighborhood not containing the other. In a T0 space, all points are topologically distinguishable.

Examples and counter examples, The Kolmogorov quotient & Operating with T0 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

Definition

Examples and counter examples

Operating with T0 spaces

The Kolmogorov quotient

Removing T0

Advanced semantic analysis

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Map overview Semantic statistics

Kolmogorov space

Nodes74
Edges73
Triples24
Avg. degree1.97
Density0.027027
Components1

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Kolmogorov space

Top relations

related to The Kolmogorov quotient · 14
Kolmogorov space → Categorically, Even, Kolmogorov, KQ, Many, No, Of, On, Only, T0, T0-ness, The, This, Topological
completely T2 · 1
Kolmogorov space → (completely Hausdorff)
T0 · 1
Kolmogorov space → (Kolmogorov)
T1 · 1
Kolmogorov space → (Fréchet)
T2 · 1
Kolmogorov space → (Hausdorff)
T2½ · 1
Kolmogorov space → (Urysohn)
T3 · 1
Kolmogorov space → (regular Hausdorff)
T3½ · 1
Kolmogorov space → (Tychonoff)
T4 · 1
Kolmogorov space → (normal Hausdorff)
T5 · 1
Kolmogorov space → (completely normal Hausdorff)

Important terminology Word statistics

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Important terminology

t0 space topological spaces points topology t1 kolmogorov set quotient distinct distinguishable every property l2 properties topologically structures hausdorff also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Kolmogorov spacecompletely T2(completely Hausdorff)1.00infobox
Kolmogorov spaceT0(Kolmogorov)1.00infobox
Kolmogorov spaceT1(Fréchet)1.00infobox
Kolmogorov spaceT2(Hausdorff)1.00infobox
Kolmogorov spaceT2½(Urysohn)1.00infobox
Kolmogorov spaceT3(regular Hausdorff)1.00infobox
Kolmogorov spaceT3½(Tychonoff)1.00infobox
Kolmogorov spaceT4(normal Hausdorff)1.00infobox
Kolmogorov spaceT5(completely normal Hausdorff)1.00infobox
Kolmogorov spaceT6(perfectly normal Hausdorff)1.00infobox
Kolmogorov spacerelated to The Kolmogorov quotientTopological0.60section
Kolmogorov spacerelated to The Kolmogorov quotientNo0.60section

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