Isomorphism definition

īsə-môrfĭzəm
A close similarity in the crystalline structure of two or more substances of similar chemical composition.
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(chem.) An identity or close similarity in the crystalline form of substances usually containing different elements but having similar composition.
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A close similarity in the crystalline structure of two or more substances of similar chemical composition.
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(math.) A one-to-one correspondence between two mathematical systems, sets, etc. that preserves the basic operations, as the correspondence between binary numbers and decimal numbers, each a set of real numbers.
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A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
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(biology) Similarity in form, as in organisms of different ancestry.
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(mathematics) A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
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(biology) Similarity in form, as in organisms of different ancestry.
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Similarity in form, as in organisms of different ancestry.
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A close similarity in the crystalline structure of two or more substances of different chemical composition. Isomorphism is seen, for example, in the group of minerals known as garnets, which can vary in chemical composition but always have the same crystal structure.
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Similarity of form.

(biology) The similarity in form of organisms of different ancestry.

(chemistry) The similarity in the crystal structures of similar chemical compounds.

(sociology) The similarity in the structure or processes of different organizations.

2. A one-to-one correspondence.

(group algebra) A bijection f such that both f and its inverse f −1 are homomorphisms, that is, structure-preserving mappings.

(computer science) A one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.

(category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).

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(biol.) A similarity in appearance or structure of organisms belonging to different species or races.
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Other Word Forms

Noun

Singular:
isomorphism
Plural:
isomorphisms

Origin of isomorphism

  • iso- +‎ -morphism

    From Wiktionary

Isomorphism Sentence Examples

  • The following table shows where isomorphism may be generally expected.

  • It is not the quantity but the quality of the anatomical and bionomic characters which determines their taxonomic value, and a few fundamental characters are better indications of the affinities of given groups of birds than a great number of agreements if these can be shown to be cases of isomorphism or heterophyletic, convergent analogy.

  • Mitscherlich, who also observed the similarity of the crystallographic characters of selenates and sulphates, which afforded valuable corroboration of his doctrine of isomorphism.

  • The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article Crystallography; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy.

  • Isomorphism may be defined as the existence of two or more different substances in the same crystal form and structure, polymorphism as the existence of the same substance in two or more crystal modifications, and morphotropy (after P. von Groth) as the change in crystal form due to alterations in the molecule of closely (chemically) related substances.

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Words near isomorphism in the Dictionary