Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30E10, 30F10

Retrieve articles in all journals with MSC: 30E10, 30F10

Additional Information

Keywords: Riemann surfaces, Behnke-Stein approximation
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society