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Importing Wikidata short description: "Class of mathematical function" (Shortdesc helper) |
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==Prior, alternate use==
Both the field of study wherein the term is used and the precise meaning of the term changed in the 20th century. In the 1930s, in [[group theory]], a ''meromorphic function'' (or ''meromorph'') was a function from a group ''G'' into itself that preserved the product on the group. The image of this function was called an ''automorphism'' of ''G''.<ref>{{cite book |last=Zassenhaus |first=Hans |author-link=Hans Zassenhaus |year=1937 |title=Lehrbuch der Gruppentheorie |publisher=B. G. Teubner Verlag |___location=Leipzig; Berlin |edition=1st |pages=29, 41}}</ref> Similarly, a ''homomorphic function'' (or ''homomorph'') was a function between groups that preserved the product, while a ''homomorphism'' was the image of a homomorph. This form of the term is now obsolete, and the related term ''meromorph'' is no longer used in group theory.
The term ''[[endomorphism]]'' is now used for the function itself, with no special name given to the image of the function. ▼
A meromorphic function is not necessarily an endomorphism, since the complex points at its poles are not in its ___domain, but may be in its range.
▲The term ''endomorphism'' is now used for the function itself, with no special name given to the image of the function.
==Properties==
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