isomorphism

[ ahy-suh-mawr-fiz-uhm ]

/ ˌaɪ səˈmɔr fɪz əm /

noun

the state or property of being isomorphous or isomorphic.

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

Origin of isomorphism

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

Words nearby isomorphism

isometropia, isometry, isomorph, isomorphic, isomorphic response, isomorphism, isomorphous, isoneph, isoniazid, isonicotinic acid hydrazide, isonome

Dictionary.com UnabridgedBased on the Random House Unabridged Dictionary, © Random House, Inc. 2020

Example sentences from the Web for isomorphism

The following table shows where isomorphism may be generally expected.
Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1|Various
Moreover, the isomorphism is simple unless for one or more operations, other than identity, the sets all remain unaltered.
Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6|Various
A subgroup of a group G, which is transformed into itself by every isomorphism of G, is called a characteristic subgroup.
Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6|Various
In this case H would contain a self-conjugate subgroup, and the isomorphism is multiple.
Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6|Various

In the first case the isomorphism is spoken of as simple, in the second as multiple.
Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6|Various

British Dictionary definitions for isomorphism

isomorphism

/ (ˌaɪsəʊˈmɔːfɪzəm) /

noun

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

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

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

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Medical definitions for isomorphism

isomorphism

[ ī′sə-môr′fĭz′əm ]

n.

A similarity in form, as in organisms of different ancestry.

A close similarity in the crystalline structure of two or more substances of similar chemical composition.

Other words from isomorphism

i′so•mor′phous adj.

Scientific definitions for isomorphism

isomorphism

[ ī′sə-môr′fĭz′əm ]

Similarity in form, as in organisms of different ancestry.

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.

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.

单词	isomorphism
释义	isomorphism [ ahy-suh-mawr-fiz-uhm ] / ˌaɪ səˈmɔr fɪz əm / noun the state or property of being isomorphous or isomorphic. Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain. Origin of isomorphism First recorded in 1820–30; isomorph(ous) + -ism Words nearby isomorphism isometropia, isometry, isomorph, isomorphic, isomorphic response, isomorphism, isomorphous, isoneph, isoniazid, isonicotinic acid hydrazide, isonome Dictionary.com UnabridgedBased on the Random House Unabridged Dictionary, © Random House, Inc. 2020 Example sentences from the Web for isomorphism The following table shows where isomorphism may be generally expected. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1\|Various Moreover, the isomorphism is simple unless for one or more operations, other than identity, the sets all remain unaltered. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6\|Various A subgroup of a group G, which is transformed into itself by every isomorphism of G, is called a characteristic subgroup. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6\|Various In this case H would contain a self-conjugate subgroup, and the isomorphism is multiple. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6\|Various In the first case the isomorphism is spoken of as simple, in the second as multiple. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6\|Various British Dictionary definitions for isomorphism isomorphism / (ˌaɪsəʊˈmɔːfɪzəm) / noun biology similarity of form, as in different generations of the same life cycle chem the existence of two or more substances of different composition in a similar crystalline form 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 Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012 Medical definitions for isomorphism isomorphism [ ī′sə-môr′fĭz′əm ] n. A similarity in form, as in organisms of different ancestry. A close similarity in the crystalline structure of two or more substances of similar chemical composition. Other words from isomorphism i′so•mor′phous adj. The American Heritage® Stedman's Medical Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. Scientific definitions for isomorphism isomorphism [ ī′sə-môr′fĭz′əm ] Similarity in form, as in organisms of different ancestry. 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. 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. The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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