Isomorphism

Isomorphism
Isomorphism I`so*mor"phism, n. [Cf. F. isomorphisme.] 1. (Crystallog.) A similarity of crystalline form between substances of similar composition, as between the sulphates of barium ({BaSO4}) and strontium ({SrSO4}). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called {hom[oe]omorphism}.

2. (Math.) A one-to-one mapping of one set onto another set which preserves the relations between the elements of the domains of the sets. [PJC]


The Collaborative International Dictionary of English. 2000.

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  • isomorphism — from Ger. Isomorphismus, 1828, coined by German chemist Eilhard Mitscherlich (1794 1863) from isomorph; see ISOMORPHIC (Cf. isomorphic). Related: Isomorph …   Etymology dictionary

  • 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 — 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 — izomorfizmas statusas T sritis chemija apibrėžtis Atomų (jonų, molekulių) gebėjimas pakeisti vienas kitą to paties tipo kristalinėje gardelėje. atitikmenys: angl. isomorphism rus. изоморфизм …   Chemijos terminų aiškinamasis žodynas

  • isomorphism — izomorfizmas statusas T sritis fizika atitikmenys: angl. isomorphism vok. Isomorphie, f rus. изоморфизм, m pranc. isomorphie, f; isomorphisme, m …   Fizikos terminų žodynas

  • isomorphism — izomorfizmas statusas T sritis augalininkystė apibrėžtis Morfologinis besikeičiančių diploidinių ir haploidinių kartų panašumas. atitikmenys: angl. isomorphism rus. изоморфизм …   Žemės ūkio augalų selekcijos ir sėklininkystės terminų žodynas

  • isomorphism — isomorphic ► ADJECTIVE ▪ corresponding in form and relations. DERIVATIVES isomorphism noun isomorphous adjective …   English terms dictionary

  • Isomorphism (disambiguation) — Isomorphism may refer to:* Isomorphism, in mathematics, a mapping that preserves the structure * Group isomorphism, in mathematics, a mapping that preserves the group structure * Ring isomorphism, in mathematics, a mapping that preserves both the …   Wikipedia

  • Isomorphism theorem — In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules,… …   Wikipedia

  • Isomorphism class — An isomorphism class is a collection of mathematical objects isomorphic with a certain mathematical object. A mathematical object usually consists of a set and some mathematical relations and operations defined over this set.Isomorphism classes… …   Wikipedia

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