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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Behnke-Stein theorem for open Riemann surfaces


Author: R. R. Simha
Journal: Proc. Amer. Math. Soc. 105 (1989), 876-880
MSC: Primary 30E10; Secondary 30F10
MathSciNet review: 953748
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Abstract: Using the Riemann-Roch theorem and the set-topological part of Bishop's special polyhedron lemma, we show that the usual Runge approximation theorem for compact subsets of the Riemann sphere is valid word-for-word on any compact Riemann surface $ X$, with meromorphic functions on $ X$ playing the role of rational functions; this result is essentially equivalent to the Behnke-Stein approximation theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0953748-X
Keywords: Riemann surfaces, Behnke-Stein approximation
Article copyright: © Copyright 1989 American Mathematical Society