Isomorphism definitions

ī'sə-môr'fĭz'əm
Similarity in form, as in organisms of different ancestry.
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A similarity in appearance or structure of organisms belonging to different species or races.
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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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A close similarity in the crystalline structure of two or more substances of similar chemical composition.
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An identity or close similarity in the crystalline form of substances usually containing different elements but having similar composition.
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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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Similarity in form, as in organisms of different ancestry.
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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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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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A close similarity in the crystalline structure of two or more substances of similar chemical composition.
noun
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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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Origin of isomorphism

iso- +‎ -morphism