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- W2036675668 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." @default.
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- W2036675668 date "1984-06-01" @default.
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- W2036675668 title "A Banach-Dieudonné theorem for germs of holomorphic functions" @default.
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- W2036675668 doi "https://doi.org/10.1016/0022-1236(84)90099-5" @default.
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