isomorphism

American  

[ahy-suh-mawr-fiz-uhm] / ˌaɪ səˈmɔr fɪz əm /

noun

1. the state or property of being isomorphous or isomorphic.

2. Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain.

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isomorphism British  

/ ˌaɪsəʊˈmɔːfɪzəm /

noun

1. biology similarity of form, as in different generations of the same life cycle

2. chem the existence of two or more substances of different composition in a similar crystalline form

3. maths a one-to-one correspondence between the elements of two or more sets, such as those of Arabic and Roman numerals, and between the sums or products of the elements of one of these sets and those of the equivalent elements of the other set or sets

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isomorphism Scientific  

/ ī′sə-môr′fĭz′əm /

1. Similarity in form, as in organisms of different ancestry.

2. 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.

3. 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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Etymology

Origin of isomorphism

First recorded in 1820–30; isomorph(ous) + -ism

Example Sentences

These proof assistants have a mechanism that mimics the common mathematical practice of transferring information about one thing to another thing that is understood to be the same via an explicit isomorphism or homotopy equivalence.

From Scientific American • Sep. 14, 2021

We can define the notion of isomorphism in any category, which allows us to transport this concept between mathematical contexts.

From Scientific American • Sep. 14, 2021

This term refers to the notion of isomorphism in the more exotic homotopy category of spaces.

From Scientific American • Sep. 14, 2021

In the category of topological spaces, the categorical notion of isomorphism is represented by an inverse pair of continuous functions.

From Scientific American • Sep. 14, 2021

If from among the set of operations S, T, U, ... which constitute a group Subgroups, conjugate operations, isomorphism, &c.

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various