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|Type:||Artigo de periódico|
|Title:||A Banach-dieudonné Theorem For Germs Of Holomorphic Functions|
|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.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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