Abstract
The aim of this paper is to characterize those locally convex spaces, which have the following properties. 1. Any curve, which is differentiable if composed with continuous linear forms, is differentiable for its own. 2. Any differentiable curve is Riemann integrable. 3. The topology is determined by the differentiable curves. 4. Linear mappings are continuous iff they are differentiable. This category of thec ∞-complete bornological spaces is symetrically monoidal closed and includes the LF-spaces.
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Unterstützt durch das Forschungsstipendium GZ 61 622/134-14/80 des Bundesministeriums für Wissenschaft und Forschung.
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Kriegl, A. Die richtigen Räume für Analysis im Unendlich-Dimensionalen. Monatshefte für Mathematik 94, 109–124 (1982). https://doi.org/10.1007/BF01301929
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DOI: https://doi.org/10.1007/BF01301929