Metrizability of spaces of holomorphic functions |
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Authors: | Jeró nimo Ló pez-Salazar |
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Affiliation: | Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Spain |
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Abstract: | In this paper we prove that if U is an open subset of a metrizable locally convex space E of infinite dimension, the space H(U) of all holomorphic functions on U, endowed with the Nachbin-Coeuré topology τδ, is not metrizable. Our result can be applied to get that, for all usual topologies, H(U) is metrizable if and only if E has finite dimension. |
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Keywords: | Holomorphic function Nachbin-Coeuré topology Bounding set Limited set |
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