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Uniform space

In the mathematical field of topology, a uniform space is a set with additional structure that is used to define uniform properties, such as completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate the weakest axioms needed for most proofs in analysis.

History, Definition & Topology of uniform spaces

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Overview

Definition

Topology of uniform spaces

Uniform continuity

Completeness

Examples

History

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Map overview Semantic statistics

Uniform space

Nodes68
Edges67
Triples87
Avg. degree1.97
Density0.029412
Components1

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Uniform space

Top relations

related to References · 27
Uniform space → Act, Berlin, Ch, Chapter II, Chapter III, Chapter IX, Convergence, Engelking, General Topology, Ind, Introduction, Isbell, ISBN, James, John, Nicolas Bourbaki, Paris, Revised, Sci, Sur
related to Examples · 12
Uniform space → Every, For, G/H, However, Indeed, Informally, One, Phi, The, Then, This, Using
see also · 11
Uniform space → Application, Coarse, Coarsest, Concept, Mathematical, Metric, Object, Structure, Type, Uniform, Uniformly
related to Completeness · 6
Uniform space → Cauchy, Generalizing, In, Instead, It, The
related to Pseudometrics definition · 6
Uniform space → Certain, For, If, More, The, Uniform
related to Topology of uniform spaces · 6
Uniform space → Compared, Every, In, Phi, The, This
related to Hausdorff completion of a uniform space · 5
Uniform space → As, Cauchy, Hausdorff, The, The Hausdorff
related to history · 5
Uniform space → Before André Weil, John Tukey, Nicolas Bourbaki, Topologie Générale, Weil
related to Uniform cover definition · 4
Uniform space → Axiomatically, If, One, Theta
related to Definition · 2
Uniform space → There, They

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Important terminology

displaystyle uniform space structure topology uniformity spaces defined entourage times topological entourages filter set pseudometrics phi every continuous metric hausdorff

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Uniform spaceis aset with additional structure that is used to define uniform properties0.90text
Uniform spacerelated to CompletenessGeneralizing0.60section
Uniform spacerelated to CompletenessInstead0.60section
Uniform spacerelated to CompletenessCauchy0.60section
Uniform spacerelated to CompletenessIn0.60section
Uniform spacerelated to CompletenessIt0.60section
Uniform spacerelated to CompletenessThe0.60section
Uniform spacerelated to DefinitionThere0.60section
Uniform spacerelated to DefinitionThey0.60section
Uniform spacerelated to ExamplesEvery0.60section
Uniform spacerelated to ExamplesIndeed0.60section
Uniform spacerelated to ExamplesThis0.60section

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