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Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that distinguish topological spaces.

Examples, Definition & Path connectedness

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Overview

Definition

Examples

Path connectedness

Arc connectedness

Local connectedness

Set operations

Theorems

Graphs

Stronger forms of connectedness

Weaker forms

Advanced semantic analysis

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Map overview Semantic statistics

Connected space

Nodes101
Edges100
Triples53
Avg. degree1.98
Density0.019802
Components1

How this topic connects Entity context

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Connected space

Top relations

related to Examples · 20
Connected space → An, Any, Banach, Euclidean, Every, For, GL, Hilbert, However, If, In, Indeed, It, More, On, Other, Sierpiński, The, The Cantor, The Sorgenfrey
related to Theorems · 9
Connected space → Arc-wise, Every, Furthermore, If, In, Let, Main, The, This
see also · 6
Connected space → Connected, Mathematics, Maximal, Property, Topological, Type
related to Local connectedness · 5
Connected space → An, It, More, Similarly, This
related to Stronger forms of connectedness · 5
Connected space → Every, If, Since, There, Yet
related to Definition · 4
Connected space → For, Otherwise, Proposition, Some
is a · 2
Connected space → stronger notion of connectedness, topological space that cannot be represented as the union of two or more disjoint non-empty open subsets
related to Path connectedness · 2
Connected space → Equivalently, The

Important terminology Word statistics

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Important terminology

connected displaystyle space two union sets path-connected topological open locally disjoint subset set path mathbb spaces every example topology disconnected

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Connected spaceis atopological space that cannot be represented as the union of two or more disjoint non-empty open subsets0.90text
Connected spaceis astronger notion of connectedness0.90text
Connected spacerelated to DefinitionOtherwise0.60section
Connected spacerelated to DefinitionSome0.60section
Connected spacerelated to DefinitionProposition0.60section
Connected spacerelated to DefinitionFor0.60section
Connected spacerelated to ExamplesThe0.60section
Connected spacerelated to ExamplesIndeed0.60section
Connected spacerelated to ExamplesEuclidean0.60section
Connected spacerelated to ExamplesIn0.60section
Connected spacerelated to ExamplesThe Sorgenfrey0.60section
Connected spacerelated to ExamplesIf0.60section

Related concept clusters Concept neighborhoods

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    Min side: 3
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