Metrizability of spaces of holomorphic functions with the Nachbin topology
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2007
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Elsevier
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Martínez Ansemil, J. M. & Ponte Miramontes, M. S. «Metrizability of Spaces of Holomorphic Functions with the Nachbin Topology». Journal of Mathematical Analysis and Applications, vol. 334, n.o 2, octubre de 2007, pp. 1146-51. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2007.01.012.
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].