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- Isomorphism abstract "In mathematics, an isomorphism, from the Greek: ἴσος isos "equal", and μορφή morphe "shape", is a homomorphism (or more generally a morphism) that admits an inverse. Two mathematical objects are isomorphic if an isomorphism exists between them. An automorphism is an isomorphism whose source and target coincide. The interest of isomorphisms lies in the fact that two isomorphic objects cannot be distinguished by using only the properties used to define morphisms; thus isomorphic objects may be considered the same as long as one considers only these properties and their consequences.For most algebraic structures, including groups and rings, a homomorphism is an isomorphism if and only if it is bijective.In topology, where the morphisms are continuous functions, isomorphisms are also called homeomorphisms or bicontinuous functions. In mathematical analysis, where the morphisms are differentiable functions, isomorphisms are also called diffeomorphisms.Isomorphisms are formalized using category theory. A morphism f : X → Y in a category is an isomorphism if it admits a two-sided inverse, meaning that there is another morphism g : Y → X in that category such that gf = 1X and fg = 1Y, where 1X and 1Y are the identity morphisms of X and Y, respectively.".
- Isomorphism thumbnail One5Root.svg?width=300.
- Isomorphism wikiPageExternalLink when_is_one.pdf.
- Isomorphism wikiPageID "14828".
- Isomorphism wikiPageRevisionID "595964089".
- Isomorphism alt "Fifth roots of unity".
- Isomorphism alt "Rotations of a pentagon".
- Isomorphism footer "The group of fifth roots of unity under multiplication is isomorphic to the group of rotations of the pentagon under composition.".
- Isomorphism hasPhotoCollection Isomorphism.
- Isomorphism id "1936".
- Isomorphism id "p/i052840".
- Isomorphism image "One5Root.svg".
- Isomorphism image "Regular polygon 5 annotated.svg".
- Isomorphism title "Isomorphism".
- Isomorphism urlname "Isomorphism".
- Isomorphism width "200".
- Isomorphism subject Category:Morphisms.
- Isomorphism comment "In mathematics, an isomorphism, from the Greek: ἴσος isos "equal", and μορφή morphe "shape", is a homomorphism (or more generally a morphism) that admits an inverse. Two mathematical objects are isomorphic if an isomorphism exists between them. An automorphism is an isomorphism whose source and target coincide.".
- Isomorphism label "Isomorfisme".
- Isomorphism label "Isomorfismo".
- Isomorphism label "Isomorfismo".
- Isomorphism label "Isomorfismo".
- Isomorphism label "Isomorphism".
- Isomorphism label "Isomorphisme".
- Isomorphism label "Isomorphismus".
- Isomorphism label "Izomorfizm".
- Isomorphism label "Изоморфизм".
- Isomorphism label "تساوي الشكل".
- Isomorphism label "同构".
- Isomorphism sameAs Izomorfismus.
- Isomorphism sameAs Isomorphismus.
- Isomorphism sameAs Isomorfismo.
- Isomorphism sameAs Isomorphisme.
- Isomorphism sameAs Isomorfismo.
- Isomorphism sameAs 동형사상.
- Isomorphism sameAs Isomorfisme.
- Isomorphism sameAs Izomorfizm.
- Isomorphism sameAs Isomorfismo.
- Isomorphism sameAs m.03twb.
- Isomorphism sameAs Q189112.
- Isomorphism sameAs Q189112.
- Isomorphism wasDerivedFrom Isomorphism?oldid=595964089.
- Isomorphism depiction One5Root.svg.
- Isomorphism isPrimaryTopicOf Isomorphism.