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A generalization of Hurwitz's Theorem
Published online by Cambridge University Press: 18 May 2009
Extract
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.
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- Copyright © Glasgow Mathematical Journal Trust 1960