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Type: Artigo de periódico
Title: A Banach-dieudonné Theorem For Germs Of Holomorphic Functions
Author: Mujica J.
Abstract: Let H(U) denote the space of all holomorphic functions on an open subset U of a complex Fréchet space E. Let H(K) denote the space of all holomorphic germs on a compact subset K of E. It is shown that H(K), with a natural topology, is the inductive limit of a suitable sequence of compact subsets, within the category of all topological spaces. As an application of this result it is shown that the compact-ported topology introduced by Nachbin coincides with the compact-open topology on H(U) whenever U is a balanced open subset of a Fréchet-Schwartz space. This last result improves earlier results of P. Boland and S. Dineen [Bull. Soc. Math. France 106 (1978), 311-336], R. Meise [Proc. Roy. Irish Acad. Sect. A 81 (1981), 217-223], and others. © 1984.
Rights: fechado
Identifier DOI: 10.1016/0022-1236(84)90099-5
Date Issue: 1984
Appears in Collections:Unicamp - Artigos e Outros Documentos

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