Die richtigen R�ume f�r Analysis im Unendlich-Dimensionalen
Copyright policy )Die richtigen R�ume f�r Analysis im Unendlich-Dimensionalen
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.
- University of Vienna Austria
- DigiZeitschriften Germany
Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, c-infinity-complete bornological spaces, Spaces defined by inductive or projective limits (LB, LF, etc.), differentiable curves in locally convex spaces, Article, 510.mathematics, Barrelled spaces, bornological spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), LF-spaces, Closed categories (closed monoidal and Cartesian closed categories, etc.), symmetrically monoidal closed, Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, c-infinity-complete bornological spaces, Spaces defined by inductive or projective limits (LB, LF, etc.), differentiable curves in locally convex spaces, Article, 510.mathematics, Barrelled spaces, bornological spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), LF-spaces, Closed categories (closed monoidal and Cartesian closed categories, etc.), symmetrically monoidal closed, Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
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