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isomorphism - 6 dictionary results

i⋅so⋅mor⋅phism

   [ahy-suh-mawr-fiz-uhm]
–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.
Origin:
1820–30; isomorph(ous) + -ism
Dictionary.com Unabridged (v 1.1)
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
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i·so·mor·phism     (ī'sə-môr'fĭz'əm)  Pronunciation Key 
n.  
  1. Biology Similarity in form, as in organisms of different ancestry.
  2. 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.
  3. A close similarity in the crystalline structure of two or more substances of similar chemical composition.

i'so·mor'phous adj.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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isomorphism

noun
(biology) similarity or identity of form or shape or structure 

WordNet® 3.0, © 2006 by Princeton University.
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isomorphism   (ī'sə-môr'fĭz'əm)  Pronunciation Key 
  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.

The American Heritage® Science Dictionary
Copyright © 2002 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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isomorphism mathematics
A bijective map between two objects which preserves, in both directions, any structure under consideration. Thus a `group isomorphism' preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on. Usually it is clear from context what sort of isomorphism is intended.
(1995-03-25)

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe
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Isomorphism

Ho`m[oe]*o*mor"phism\, n. [See Hom[oe]omorphous.] A near similarity of crystalline forms between unlike chemical compounds. See Isomorphism.

Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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