Categorical differential calculus for infinite dimensional spaces
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 29 (1988) no. 4, pp. 257-286. 
@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},
     pages = {257--286},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {29},
     number = {4},
     year = {1988},
     mrnumber = {991203},
     zbl = {0678.46034},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_1988__29_4_257_0/}
}
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Nel, L. D. Categorical differential calculus for infinite dimensional spaces. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 29 (1988) no. 4, pp. 257-286. http://archive.numdam.org/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

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

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

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

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

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

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

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

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 | Zbl

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

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 | Zbl

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

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 | Zbl

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 | Zbl

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 | Zbl

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

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

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

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