isomorphism of two sets

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• Isomorphism — In abstract algebra, an isomorphism (Greek: ἴσος isos equal , and μορφή morphe shape ) is a bijective map f such that both f and its inverse f −1 are homomorphisms, i.e., structure preserving mappings.In the more general setting of category… …   Wikipedia

• Isomorphism (biology) — For other uses of isomorphism, see isomorphism (disambiguation). In biology, an isomorphism is a similarity of form or structure between organisms. The term isomorphism is borrowed from mathematical usage, where it refers to a one to one mapping… …   Wikipedia

• isomorphism — /uy seuh mawr fiz euhm/, n. 1. the state or property of being isomorphous or isomorphic. 2. Math. a one to one relation onto the map between two sets, which preserves the relations existing between elements in its domain. [1820 30; ISOMORPH(OUS)… …   Universalium

• isomorphism — i•so•mor•phism [[t]ˌaɪ səˈmɔr fɪz əm[/t]] n. 1) bio chem. cry the state or property of being isomorphous or isomorphic 2) math. Math. a one to one relation onto the map between two sets, which preserves the relations existing between elements in… …   From formal English to slang

• isomorphism — [ī΄sō môr′fiz΄əm, ī΄sə môr′fiz΄əm] n. [< ISOMORPHIC + ISM] 1. Biol. a similarity in appearance or structure of organisms belonging to different species or races 2. Chem. an identity or close similarity in the crystalline form of substances… …   English World dictionary

• Isomorphism of categories — In category theory, two categories C and D are isomorphic if there exist functors F : C rarr; D and G : D rarr; C which are mutually inverse to each other, i.e. FG = 1 D (the identity functor on D ) and GF = 1 C . This means that both the objects …   Wikipedia

• isomorphism — noun Etymology: International Scientific Vocabulary Date: circa 1828 1. the quality or state of being isomorphic: as a. similarity in organisms of different ancestry resulting from convergence b. similarity of crystalline form between chemical… …   New Collegiate Dictionary

• Group isomorphism — In abstract algebra, a group isomorphism is a function between two groups that sets up a one to one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two… …   Wikipedia

• Myhill isomorphism theorem — For the Goodman–Myhill theorem in constructive set theory, see Diaconescu s theorem. In computability theory the Myhill isomorphism theorem, named after John Myhill, provides a characterization for two numberings to induce the same notion of… …   Wikipedia

• Computable isomorphism — In computability theory two sets A and B are computably isomorphic or recursively isomorphic if there exists a bijective computable function f with f(A) = B. Two numberings ν and μ are called computably isomorphic if there exists a bijective… …   Wikipedia

• Graph isomorphism — In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H. This kind of bijection is commonly… …   Wikipedia