Retraction (topology)
In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrinking a space into a subspace. An absolute neighborhood retract (ANR) is a particularly well-behaved type of topological space. For example, every topological manifold is an ANR. Every ANR has the homotopy type of a very simple topological space, a CW complex.
Wikipage disambiguates
ANRAbsolute neighborhood retractAbsolute retractBing–Borsuk conjectureBrouwer fixed-point theoremCategory of topological spacesCellular approximation theoremCofibrationComb spaceConfiguration space (mathematics)Contractible spaceDe Rham cohomologyDefamation retractionDeformation (engineering)Deformation retractDeformation retractionDiffeomorphismDominant functorDual objectDunce hat (topology)Eilenberg–Steenrod axiomsExcision theoremExtended natural numbersExtremally disconnected spaceFibrationFixed-point propertyFixed point (mathematics)Franz-Erich WolterG-structure on a manifoldGelfand ringGlossary of algebraic topologyGram–Schmidt processHomotopyHomotopy extension propertyHomotopy fiberInclusion mapInduced homomorphismInfinite broomJordan curve theoremKakutani fixed-point theorem
Link from a Wikipage to another Wikipage
primaryTopic
Retraction (topology)
In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrinking a space into a subspace. An absolute neighborhood retract (ANR) is a particularly well-behaved type of topological space. For example, every topological manifold is an ANR. Every ANR has the homotopy type of a very simple topological space, a CW complex.
has abstract
En topologie générale et surto ...... cissement » de façon continue.
@fr
In matematica, più precisament ...... lle sue proprietà topologiche.
@it
In topology, a branch of mathe ...... pological space, a CW complex.
@en
Retrakt deformacyjny – specjal ...... w sposób ciągły „skurczyć” do
@pl
В математиці, а саме в тополог ...... гомотопій і теорії гомологій.
@uk
Деформационный ретракт тополог ...... огим деформационным ретрактом.
@ru
في الطوبولوجيا، وهو أحد فروع ا ...... ضاء إلى أن يصبح فضاءً ثانويًا.
@ar
位相幾何学という数学の分野において，レトラクション (ret ...... R は非常に単純な位相空間，CW複体，のホモトピー型を持つ．
@ja
在拓扑学中，收缩（retraction），顾名思义是将整个空间收缩到一个子空间；形变收缩（deformation retraction）是将空间“连续收缩”成一个子空间的映射。
@zh
호모토피 이론에서, 변형 수축(變形收縮, 영어: def ...... 모든 호모토피 동치는 변형 수축들로 나타낼 수 있다.
@ko
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,021,191,351
Link from a Wikipage to another Wikipage
title
Neighborhood retract
@en
wikiPageUsesTemplate
subject
comment
En topologie générale et surto ...... cissement » de façon continue.
@fr
In matematica, più precisament ...... lle sue proprietà topologiche.
@it
In topology, a branch of mathe ...... pological space, a CW complex.
@en
Retrakt deformacyjny – specjal ...... w sposób ciągły „skurczyć” do
@pl
В математиці, а саме в тополог ...... гомотопій і теорії гомологій.
@uk
Деформационный ретракт тополог ...... огим деформационным ретрактом.
@ru
في الطوبولوجيا، وهو أحد فروع ا ...... ضاء إلى أن يصبح فضاءً ثانويًا.
@ar
位相幾何学という数学の分野において，レトラクション (ret ...... R は非常に単純な位相空間，CW複体，のホモトピー型を持つ．
@ja
在拓扑学中，收缩（retraction），顾名思义是将整个空间收缩到一个子空间；形变收缩（deformation retraction）是将空间“连续收缩”成一个子空间的映射。
@zh
호모토피 이론에서, 변형 수축(變形收縮, 영어: def ...... 모든 호모토피 동치는 변형 수축들로 나타낼 수 있다.
@ko
label
Retraction (topology)
@en
Retrakt deformacyjny
@pl
Retrazione
@it
Rétraction
@fr
Деформационный ретракт
@ru
Ретракт
@uk
انكماش تشويهي
@ar
レトラクト (位相幾何学)
@ja
形变收缩
@zh
변형 수축
@ko