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Metrizability of spaces of holomorphic functions with the Nachbin topology

Ansemil, José María M. and Ponte, Socorro (2007) Metrizability of spaces of holomorphic functions with the Nachbin topology. Journal of Mathematical Analysis and Applications, 334 (2). pp. 1146-1151. ISSN 0022-247X

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Abstract

In this paper we prove, among other things, that the space of all holomorphic functions on an open subset U of a complex metrizable space E, endowed with the Nachbin ported topology, is metrizable only if E has finite dimension. This answers a question by Mujica in [J. Mujica, Germenes holomorfos y funciones holomorfas en espacios de Frechet, Publicaciones del Departamento de Teoria de Funciones, Universidad de Santiago, Spain, 1978].


Item Type:Article
Uncontrolled Keywords:holomorphic function; nachbin topology; metrizable space
Subjects:Sciences > Mathematics > Functions
ID Code:16791
References:

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Deposited On:22 Oct 2012 09:14
Last Modified:07 Feb 2014 09:35

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