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Homotopy

In topology, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós 'same, similar' and τόπος tópos 'place') if one can be "continuously deformed" into the other, such a deformation being called a homotopy (/həˈmɒtəpiː/ hə-MOT-ə-pee; /ˈhoʊmoʊˌtoʊpiː/ HOH-moh-toh-pee) between the two functions.…

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Overview

Formal definition

Properties

Examples

Homotopy equivalence

Invariance

Variants

Applications

Sources

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Map overview Semantic statistics

Homotopy

Nodes109
Edges108
Triples89
Avg. degree1.98
Density0.018349
Components1

How this topic connects Entity context

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Homotopy

Top relations

has application · 12
Homotopy → Based, CW, CW-complex, Eilenberg, Eilenberg-MacLane, For, Hopf, MacLane, One, The, Using, Whitney
related to Examples · 12
Homotopy → Any, CW, Euclidean, Every, If, Let, More, The, Then, There, This, X/A
related to Sources · 12
Homotopy → Algebraic Topology, Armstrong, Basic Topology, December, Edwin, EMS Press, Encyclopedia, ISBN, Isotopy, Mathematics, Spanier, Springer
related to Homotopy category · 6
Homotopy → For, Hn, Likewise, The, Then, Two
related to Groups · 5
Homotopy → If, In, Since, These, We
related to Homotopy equivalence · 5
Homotopy → Given, If, Intuitively, Spaces, This
related to Relative homotopy · 5
Homotopy → Also, Formally, In, These, When
related to Homotopy equivalence vs. homeomorphism · 4
Homotopy → But, Some, The Möbius, Therefore
related to Invariance · 4
Homotopy → For, If, The, Without
related to Lifting and extension properties · 4
Homotopy → Another, If, It, The

Important terminology Word statistics

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Important terminology

displaystyle equivalence two continuous space map equivalent one homotopic spaces algebraic function example mathbb isotopy topology maps times identity functions

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Homotopyis adefinition of homotopy groups and cohomotopy groups0.90text
Homotopyis ahomotopy extension property0.90text
the 3-sphere can be simply connectedinstance ofA manifold0.80text
Homotopyhas applicationBased0.60section
Homotopyhas applicationThe0.60section
Homotopyhas applicationFor0.60section
Homotopyhas applicationCW-complex0.60section
Homotopyhas applicationEilenberg0.60section
Homotopyhas applicationMacLane0.60section
Homotopyhas applicationOne0.60section
Homotopyhas applicationEilenberg-MacLane0.60section
Homotopyhas applicationUsing0.60section

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