Geodesic
A generalization of Hurwitz's Theorem
Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 101-102

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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. 
Husemoller, Dale H. A generalization of Hurwitz's Theorem. Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 101-102. doi: 10.1017/S2040618500033980
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[1] 1.Ahlfors, L. V., Complex analysis (New York, 1953). Google Scholar

[2] 2.Bourbaki, N., Topologie générale (Paris, 1949), Chap. X, §2. Google Scholar

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