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Convenient Vector Spaces of Smooth Functions
Author(s) -
Kriegl A.,
Nel L. D.
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901470105
Subject(s) - mathematics , locally convex topological vector space , vector space , space (punctuation) , pure mathematics , principal (computer security) , regular polygon , vector (molecular biology) , vector valued function , function space , normed vector space , interpolation space , algebra over a field , mathematical analysis , functional analysis , topological space , geometry , computer science , biochemistry , operating system , chemistry , gene , recombinant dna
By a convenient vector space is meant a locally convex IR‐vector space which is separated, bornological and Mackey‐complete. The theory of such spaces, initiated in [Kr 82], [Fr 82], and [FGK 83], has evolved into a book [FK 88]. In the preliminaries below we outline the principal features of this theory relevant to this paper. We are concerned mainly with questions about the reflexiveness of spaces C ∞ ( X , ℝ) for various X and matters closely related to this.