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A generalization of Hurwitz's Theorem

Published online by Cambridge University Press:  18 May 2009

Dale H. Husemoller
Dale H. Husemoller
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania, U.S.A.
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Hurwitz's theorem says that the limit of schlicht functions, in the topology of compact convergence, is again a schlicht function or a constant function. We generalize this to mappings between Riemann surfaces and get more precise information on the relation between the distribution of values of analytic functions and the topology of compact convergence on the space of all analytic maps.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 3 , January 1960 , pp. 101 - 102
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

References

1.Ahlfors, L. V., Complex analysis (New York, 1953).Google Scholar
2.Bourbaki, N., Topologie générale (Paris, 1949), Chap. X, §2.Google Scholar