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Metrizability of spaces of holomorphic functions with the Nachbin topology
- Source :
-
Journal of Mathematical Analysis & Applications . Oct2007, Vol. 334 Issue 2, p1146-1151. 6p. - Publication Year :
- 2007
-
Abstract
- 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, Gérmenes holomorfos y funciones holomorfas en espacios de Fréchet, Publicaciones del Departamento de Teoría de Funciones, Universidad de Santiago, Spain, 1978]. [Copyright &y& Elsevier]
- Subjects :
- *LINEAR algebra
*GEOMETRY
*MATHEMATICS
*EUCLID'S elements
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 334
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 25488795
- Full Text :
- https://doi.org/10.1016/j.jmaa.2007.01.012