J Austral Math Soc Ser A 59 pp287--303, 1995.

The Locally Convex Topology on the Space of Meromorphic Functions

Karl-Goswin Grosse-Erdmann

Abstract

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 result 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 Holdgrun 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 Holdgrun's topology is the natural locally convex topology on the space of meromorphic functions.

1991 AMS Subject Classification: primary 30D30, 46E10; secondary 12J99

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Authors

Karl-Goswin Grosse-Erdmann

Fachbereich Mathematik, Fernuniversitat Hagen, Postfach 940, D-58084 Hagen, Germany.