Categorical differential calculus for infinite dimensional spaces
Nel, L. D.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 29 (1988), p. 257-286 / Harvested from Numdam
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Publié le : 1988-01-01
@article{CTGDC_1988__29_4_257_0,
     author = {Nel, L. D.},
     title = {Categorical differential calculus for infinite dimensional spaces},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {29},
     year = {1988},
     pages = {257-286},
     mrnumber = {991203},
     zbl = {0678.46034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1988__29_4_257_0}
}

Nel, L. D. Categorical differential calculus for infinite dimensional spaces. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 29 (1988) pp. 257-286. http://gdmltest.u-ga.fr/item/CTGDC_1988__29_4_257_0/

1 V.I. Averbukh and O.G. Smolyanov: The various definitions of the derivative in linear topological spaces. Russian Math. Surveys 23 (1968) 67-113. | Zbl 0196.15702

2 A. Bastiani, Applications différentiables et variétés différentiable de dimension infini, J. Analyse Math. 13 (1964) 1-114. | MR 177277 | Zbl 0196.44103

3 Ernst Binz, Continuous convergence on C(X), Lecture Notes in Math. 469 (Springer, Berlin, 1975). | MR 461418 | Zbl 0306.54003

4 H.-P. Butzmann, Über die c-Reflexivität von Cc(X), Comment. Math. Helv.(1972) 92-101. | MR 308651 | Zbl 0237.46026

5 G. Choquet, Convergences, Ann. Univ. Grenoble 23 (1947/48) 57-112. | Numdam | MR 25716 | Zbl 0031.28101

6 A. Frölicher and A. Kriegl, Linear spaces and differentiation theory (J. Wiley, New York, 1988?) | MR 961256 | Zbl 0657.46034

7 R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (1982) 65-222. | MR 656198 | Zbl 0499.58003

8 H. Herrlich and G.E. Strecker, Category Theory (Heldermann, Berlin, 1979). | MR 571016 | Zbl 0437.18001

9 H.H. Keller, Ueber Probleme, die bei einer Differentialrechnung in topologischen Vektorräumen auftreten. Festband z. 70. Geburtstag v. Rolf Nevanlinna, (Springer Berlin 1966) 49-57. | MR 223887 | Zbl 0156.38401

10 H.H. Keller, Differential Calculus in Locally Convex Spaces, Lecture Notes in Math. 417 (Springer, Berlin, 1974). | MR 440592 | Zbl 0293.58001

11 A. Kriegl and L.D. Nel, A convenient setting for holomorphy, Cahiers de topologie et géometrie différentielle catégoriques 26 (1985) 273-309. | Numdam | MR 796352 | Zbl 0581.46041

12 A. Kriegl and L.D. Nel, Convenient vector spaces of smooth functions Math. Nachr. (to appear). | MR 1127307 | Zbl 0752.46027

13 L.D. Nel, Convenient topological algebra and reflexive objects, Categorical Topology, Proc. Int. Conf. Berlin 1978, Lecture Notes in Math. (Springer) 719 (1979) 259-276. | MR 544652 | Zbl 0416.18013

14 L.D. Nel, Enriched algebraic structures with applications in Functional Analysis, Categorical Aspects of Topology and Analysis, Proc. Int. Conf. Carleton Univ.1980, Lecture Notes in Math. (Springer) 915 (1982) 247-259. | MR 659896 | Zbl 0482.18003

15 L.D. Nel, Topological universes and smooth Gelfand-Naimark duality, Mathematical applications of category theory, Proc. A. M. S. Spec. Session Denver, 1983, Contemporary Mathematics 30 (1984) 224-276. | MR 749775 | Zbl 0548.46054

16 L.D. Nel, Upgrading functional analytic categories, Proc. Toledo Int. Conf. 1983 (Heldermann, Berlin, 1984) 408-424. | MR 785026 | Zbl 0555.46034

17 L.D. Nel, Enriched locally convex structures, calculus and Riesz representations, J. Pure Appl. Algebra 42 (1986) 165-184. | MR 857565 | Zbl 0608.46045

18 L.D. Nel, Optimal subcategories and Stone-Weierstrass, Topology and Appl. 27 (1987) 191-200. | MR 911691 | Zbl 0641.46050

19 U. Seip, A convenient setting for differential calculus, J. Pure Appl. Algebra 14 (1979) 73-100. | MR 515488 | Zbl 0397.58014