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Uniform continuity

In mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle \delta } such that function values over any function domain interval of the size δ {\displaystyle \delta } are as close to each other as we want. In other words, for a uniformly continuous real…

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Overview

Definition for functions on metric spaces

Local continuity versus global uniform continuity

Properties

Examples and nonexamples

History

Other characterizations

Relations with the extension problem

Generalization to topological vector spaces

Generalization to uniform spaces

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Map overview Semantic statistics

Uniform continuity

Nodes60
Edges59
Triples75
Avg. degree1.97
Density0.033333
Components1

How this topic connects Entity context

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Uniform continuity

Top relations

related to Further reading · 41
Uniform continuity → Academic Press, Advanced Calculus, Bolzano, Bourbaki, Brooks/Cole, Chapter II, Chapters, Date, Dieudonné, EMS PressRudin, Encyclopedia, Fitzpatrick, Foundations, General, General Topology, Graduate Texts, Historia Mathematica, ISBN, Jean, John
related to Characterization via sequences · 5
Uniform continuity → Euclidean, Fitzpatrick, For, If, More
related to history · 5
Uniform continuity → Bolzano, Dirichlet, Heine, In, The
related to Properties · 5
Uniform continuity → But, Consider, Every, Given, This
related to Generalization to topological vector spaces · 4
Uniform continuity → Banach, For, In, This
related to Local continuity versus global uniform continuity · 4
Uniform continuity → Continuity, In, On, When
related to Non-standard analysis · 4
Uniform continuity → In, Note, Thus, Uniform
is a · 3
Uniform continuity → global property of f, rather strong condition, stronger continuity condition than continuity
related to Generalization to uniform spaces · 3
Uniform continuity → Cauchy, In, Just
related to Definition for functions on metric spaces · 1
Uniform continuity → For

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Important terminology

continuous displaystyle function uniformly continuity uniform real delta every interval functions varepsilon number spaces metric point exists positive space numbers

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Uniform continuityis astronger continuity condition than continuity0.90text
Uniform continuityis aglobal property of f0.90text
Uniform continuityis arather strong condition0.90text
Uniform continuityrelated to Characterization via sequencesFor0.60section
Uniform continuityrelated to Characterization via sequencesEuclidean0.60section
Uniform continuityrelated to Characterization via sequencesFitzpatrick0.60section
Uniform continuityrelated to Characterization via sequencesMore0.60section
Uniform continuityrelated to Characterization via sequencesIf0.60section
Uniform continuityrelated to Definition for functions on metric spacesFor0.60section
Uniform continuityrelated to Further readingLock-green0.60section
Uniform continuityrelated to Further readingLock-gray-alt-20.60section
Uniform continuityrelated to Further readingLock-red-alt-20.60section

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