Meromorphic function: Difference between revisions

Revision as of 21:01, 24 December 2019

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From an algebraic point of view, if the functions' ___domain is [[connected set|connected]], then the set of meromorphic functions is the [[field of fractions]] of the [[integral ___domain]] of the set of holomorphic functions. This is analogous to the relationship between the [[rational number]]s and the [[integer]]s.

==Prior, alternate use==

==History==

The field of study where the term is used and the specific meaning of the term changed in the 20th&nbsp;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.