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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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Kolmogorov space at a glance

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Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

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

Topics to explore

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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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How this topic connects Entity context

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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

Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.
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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    Map overview Semantic statistics

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    Kolmogorov space

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