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Metrizability of spaces of holomorphic functions with the Nachbin topology

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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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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X07000339


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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
Deposited On:22 Oct 2012 09:14
Last Modified:10 Aug 2018 09:03

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