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Hyperconnected space

In the mathematical field of topology, a hyperconnected space or irreducible space is a topological space X that cannot be written as the union of two proper closed subsets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry.

Examples, Properties & Irreducible components

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Overview

Examples

Hyperconnectedness vs. connectedness

Properties

Irreducible components

Advanced semantic analysis

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Map overview Semantic statistics

Hyperconnected space

Nodes49
Edges48
Triples37
Avg. degree1.96
Density0.040816
Components1

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Hyperconnected space

Top relations

related to References · 22
Hyperconnected space → Arthur Jr, Berlin, Counterexamples, Dover, Elsevier/North-Holland, Encyclopedia, Hart, Hyperconnected, ISBN, Jerry, Jun-iti, Klaas Pieter, Lynn Arthur, MR, Nagata, New York, PlanetMath, Seebach, Springer-Verlag, Steen
related to Properties · 8
Hyperconnected space → Every, Hausdorff, In, It, More, Since, The, Thus
related to Examples · 3
Hyperconnected space → For, In, Two
related to Hyperconnectedness vs. connectedness · 3
Hyperconnected space → Every, Note, This
is a · 1
Hyperconnected space → whole space

Important terminology Word statistics

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Important terminology

space irreducible hyperconnected every open set two disjoint closed subset topological nonempty connected topology sets components union dense hausdorff displaystyle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperconnected spaceis awhole space0.90text
Hyperconnected spacerelated to ExamplesTwo0.60section
Hyperconnected spacerelated to ExamplesIn0.60section
Hyperconnected spacerelated to ExamplesFor0.60section
Hyperconnected spacerelated to Hyperconnectedness vs. connectednessEvery0.60section
Hyperconnected spacerelated to Hyperconnectedness vs. connectednessNote0.60section
Hyperconnected spacerelated to Hyperconnectedness vs. connectednessThis0.60section
Hyperconnected spacerelated to PropertiesThe0.60section
Hyperconnected spacerelated to PropertiesThus0.60section
Hyperconnected spacerelated to PropertiesHausdorff0.60section
Hyperconnected spacerelated to PropertiesEvery0.60section
Hyperconnected spacerelated to PropertiesSince0.60section

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    Min side: 3
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