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Behnke-Stein theorem on complex spaces with singularities

Published online by Cambridge University Press:  22 January 2016

M. Colţoiu  and
A. Silva
M. Colţoiu
Affiliation:
Institute of Mathematics of the Romanian Academy, P. 0. Box 1-764 RO-70700 Bucharest, Romania
A. Silva
Affiliation:
Dipartimento di Matematica, “G. Castelnuovo” Università di Roma “La Sapienza” 1-00185 Roma, Italy
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Let X be a non-compact Riemann surface and D ⊂ X an open subset. By a classical result due to Behnke and Stein [2] D is Runge in X (i.e. the restriction map has dense image) iff X\D has no compact connected components. In other words the obstruction to holomorphic approximation is purely topological. This result has been generalized to 1-dimensional Stein spaces by Mihalache in [11].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 137 , March 1995 , pp. 183 - 194
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

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