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The locally convex topology on the space of meromorphic functions

Part of: Linear function spaces and their duals Entire and meromorphic functions, and related topics Topological fields

Published online by Cambridge University Press:  09 April 2009

Karl-Goswin Grosse-Erdmann
Karl-Goswin Grosse-Erdmann
Affiliation:
Fachbereich Mathematik FernuniversitätHagen Postfach 940 D-58084 Hagen, Germany
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Abstract

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We give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.

MSC classification

Secondary: 30D30: Meromorphic functions, general theory 46E10: Topological linear spaces of continuous, differentiable or analytic functions 12J99: None of the above, but in this section 46E25: Rings and algebras of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 287 - 303
Copyright
Copyright © Australian Mathematical Society 1995

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