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 $A$ and $B$ are structures of a certain species such that there exists an isomorphism $A\to B$, then $A$ and $B$ 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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