Die richtigen Räume für Analysis im Unendlich-Dimensionalen. (German) Zbl 0489.46035
MSC:
| 46G05 | Derivatives of functions in infinite-dimensional spaces |
| 46A08 | Barrelled spaces, bornological spaces |
| 26E20 | Calculus of functions taking values in infinite-dimensional spaces |
| 46A13 | Spaces defined by inductive or projective limits (LB, LF, etc.) |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
| 46A30 | Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) |
| 18D15 | Closed categories (closed monoidal and Cartesian closed categories, etc.) |
Keywords:
differentiable curves in locally convex spaces; c-infinity-complete bornological spaces; symmetrically monoidal closed; LF-spacesReferences:
| [1] | Boman, J.: Differentiability of a function and of its composition with functions of one variable. Math. Scand.20, 249-268 (1967). · Zbl 0182.38302 |
| [2] | Frölicher, A.: Applications lisses entre espaces et variétés de Fréchet. Preprint. 1981. · Zbl 0471.46028 |
| [3] | Herrlich, H., Strecker, G.: Category Theory. Boston: Allyn and Bacon. 1973. · Zbl 0265.18001 |
| [4] | Hogbe-Nlend, H.: Complétion, tenseurs, nucléarité en bornologie. J. Math. Pures Appl. (9)49, 193-288 (1970). · Zbl 0199.18001 |
| [5] | Hogbe-Nlend, H.: Bornologies and Functional Analysis. Amsterdam: North Holland. 1977. · Zbl 0359.46004 |
| [6] | Keller, H. H.: Differential Calculus in Locally Convex Spaces. Lect. Notes Math. 417. Berlin-Heidelberg-New York: Springer. 1974. · Zbl 0293.58001 |
| [7] | Kriegl, A.: Eine Theorie glatter Mannigfaltigkeiten und Vektorbündel. Dissertation. Wien. 1980. · Zbl 0476.58003 |
| [8] | Schaefer, H. H.: Topological Vector Spaces. New York-Heidelberg-Berlin: Springer. 1970. · Zbl 0203.43002 |
| [9] | Seip, U.: A convenient setting for smooth manifolds. J. Pure Appl. Alg.21, 279-305 (1981). · Zbl 0463.58001 · doi:10.1016/0022-4049(81)90020-7 |
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