Difference between revisions of "Isomorphism"
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An '''isomorphism''' is a [[bijective]] [[homomorphism]]. If <math>A</math> and <math>B</math> are structures of a certain species such that there exists an isomorphism <math>A\to B</math>, then <math>A</math> and <math>B</math> are said to be '''isomorphic''' structures of that species. Informally speaking, two isomorphic structures can be considered as two superficially different versions of the same structure. | An '''isomorphism''' is a [[bijective]] [[homomorphism]]. If <math>A</math> and <math>B</math> are structures of a certain species such that there exists an isomorphism <math>A\to B</math>, then <math>A</math> and <math>B</math> are said to be '''isomorphic''' structures of that species. Informally speaking, two isomorphic structures can be considered as two superficially different versions of the same structure. | ||
Revision as of 18:42, 12 March 2008
| This is an AoPSWiki Word of the Week for March 12-19 |
An isomorphism is a bijective homomorphism. If 
and 
are structures of a certain species such that there exists an isomorphism 
, then and are said to be isomorphic structures of that species. Informally speaking, two isomorphic structures can be considered as two superficially different versions of the same structure.
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