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Continuous function

In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting its argument to…

History, Real functions & Continuous functions between topological spaces

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Real functions

Real functionGraphCartesian planeCurveDomain
33 related topics

Continuous functions between topological spaces

SubsetsOpen ballsPreimagesClosed setsDiscrete topology
24 related topics

Related notions

RestrictsTietze extension theoremHahn–Banach theoremDense subsetBlumberg theorem
24 related topics

Continuous functions between metric spaces

MetricTriangle inequalityCauchy sequenceG δ {\displaystyle G_{\delta }} setFunctional analysis
16 related topics

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Overview

History

Real functions

Properties

Continuous functions between metric spaces

Continuous functions between topological spaces

Related notions

Bibliography

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Continuous function

Nodes211
Edges210
Triples55
Avg. degree1.99
Density0.009479
Components1

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Continuous function

Top relations

related to Bibliography · 12
Continuous function → Allyn, Bacon, Boston, Continuous, Dugundji, EMS Press, Encyclopedia, ISBN, James, Mathematics, OCLC, Topology
related to Related notions · 12
Continuous function → Banach, For, Hahn, Hausdorff, Here, If, In, Scott, The Blumberg, This, Tietze, Various
related to Uniform, Hölder and Lipschitz continuity · 12
Continuous function → Any Hölder, Hölder, Intuitively, Lindelöf, Lipschitz, More, Picard, That, The, The Lipschitz, Thus, Uniformly
related to Examples of discontinuous functions · 5
Continuous function → An, Heaviside, Intuitively, Pick, Then
related to Directional continuity · 4
Continuous function → Discontinuous, For, Formally, Roughly
related to Homeomorphisms · 4
Continuous function → Given, Hausdorff, If, Symmetric
see also · 4
Continuous function → Absolute, Continuity, Continuous, Direction-preserving
is a · 1
Continuous function → function such that a small variation of its argument induces at most a small variation of its value
related to Alternative definitions · 1
Continuous function → Several

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Important terminology

continuous displaystyle function continuity functions point domain delta every defined limit spaces topological definition topology set metric subset right varepsilon

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Continuous functionis afunction such that a small variation of its argument induces at most a small variation of its value0.90text
Continuous functionrelated to Alternative definitionsSeveral0.60section
Continuous functionrelated to BibliographyDugundji0.60section
Continuous functionrelated to BibliographyJames0.60section
Continuous functionrelated to BibliographyTopology0.60section
Continuous functionrelated to BibliographyBoston0.60section
Continuous functionrelated to BibliographyAllyn0.60section
Continuous functionrelated to BibliographyBacon0.60section
Continuous functionrelated to BibliographyISBN0.60section
Continuous functionrelated to BibliographyOCLC0.60section
Continuous functionrelated to BibliographyContinuous0.60section
Continuous functionrelated to BibliographyEncyclopedia0.60section

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