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Totally bounded space

In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered by finitely many subsets of every fixed “size” (where the meaning of “size” depends on the structure of the ambient space).

In topological groups, In metric spaces & Examples and elementary properties

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In topological groups

21 related topics

In metric spaces

15 related topics

Examples and elementary properties

13 related topics

Overview

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In metric spaces

Examples and elementary properties

In topological groups

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Totally bounded space

Nodes68
Edges67
Triples7
Avg. degree1.97
Density0.029412
Components1

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Totally bounded space

Top relations

related to In metric spaces · 7
Totally bounded space → Cauchy, Each, Equivalently, Euclidean, For, The, This

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Important terminology

bounded totally displaystyle space set compact metric subset sets every finite cl spaces definition topological subsets holds left operatorname complete

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SubjectPredicateObjectConfidenceSrc
Totally bounded spacerelated to In metric spacesEquivalently0.60section
Totally bounded spacerelated to In metric spacesThis0.60section
Totally bounded spacerelated to In metric spacesCauchy0.60section
Totally bounded spacerelated to In metric spacesEach0.60section
Totally bounded spacerelated to In metric spacesThe0.60section
Totally bounded spacerelated to In metric spacesEuclidean0.60section
Totally bounded spacerelated to In metric spacesFor0.60section

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