Categorical differential calculus for infinite dimensional spaces

L. D. Nel

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1988)

  • Volume: 29, Issue: 4, page 257-286
  • ISSN: 1245-530X

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Nel, L. D.. "Categorical differential calculus for infinite dimensional spaces." Cahiers de Topologie et Géométrie Différentielle Catégoriques 29.4 (1988): 257-286. <http://eudml.org/doc/91426>.

@article{Nel1988,
author = {Nel, L. D.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {categorical differential calculus; exponential rule},
language = {eng},
number = {4},
pages = {257-286},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Categorical differential calculus for infinite dimensional spaces},
url = {http://eudml.org/doc/91426},
volume = {29},
year = {1988},
}

TY - JOUR
AU - Nel, L. D.
TI - Categorical differential calculus for infinite dimensional spaces
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1988
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 29
IS - 4
SP - 257
EP - 286
LA - eng
KW - categorical differential calculus; exponential rule
UR - http://eudml.org/doc/91426
ER -

References

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  2. 2 A. Bastiani, Applications différentiables et variétés différentiable de dimension infini, J. Analyse Math.13 (1964) 1-114. Zbl0196.44103MR177277
  3. 3 Ernst Binz, Continuous convergence on C(X), Lecture Notes in Math.469 (Springer, Berlin, 1975). Zbl0306.54003MR461418
  4. 4 H.-P. Butzmann, Über die c-Reflexivität von Cc(X), Comment. Math. Helv.(1972) 92-101. Zbl0237.46026MR308651
  5. 5 G. Choquet, Convergences, Ann. Univ. Grenoble23 (1947/48) 57-112. Zbl0031.28101MR25716
  6. 6 A. Frölicher and A. Kriegl, Linear spaces and differentiation theory (J. Wiley, New York, 1988?) Zbl0657.46034MR961256
  7. 7 R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (1982) 65-222. Zbl0499.58003MR656198
  8. 8 H. Herrlich and G.E. Strecker, Category Theory (Heldermann, Berlin, 1979). Zbl0437.18001MR571016
  9. 9 H.H. Keller, Ueber Probleme, die bei einer Differentialrechnung in topologischen Vektorräumen auftreten. Festband z. 70. Geburtstag v. Rolf Nevanlinna, (SpringerBerlin1966) 49-57. Zbl0156.38401MR223887
  10. 10 H.H. Keller, Differential Calculus in Locally Convex Spaces, Lecture Notes in Math.417 (Springer, Berlin, 1974). Zbl0293.58001MR440592
  11. 11 A. Kriegl and L.D. Nel, A convenient setting for holomorphy, Cahiers de topologie et géometrie différentielle catégoriques26 (1985) 273-309. Zbl0581.46041MR796352
  12. 12 A. Kriegl and L.D. Nel, Convenient vector spaces of smooth functionsMath. Nachr. (to appear). Zbl0752.46027MR1127307
  13. 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. Zbl0416.18013MR544652
  14. 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. Zbl0482.18003MR659896
  15. 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 Mathematics30 (1984) 224-276. Zbl0548.46054MR749775
  16. 16 L.D. Nel, Upgrading functional analytic categories, Proc. Toledo Int. Conf. 1983 (Heldermann, Berlin, 1984) 408-424. Zbl0555.46034MR785026
  17. 17 L.D. Nel, Enriched locally convex structures, calculus and Riesz representations, J. Pure Appl. Algebra42 (1986) 165-184. Zbl0608.46045MR857565
  18. 18 L.D. Nel, Optimal subcategories and Stone-Weierstrass, Topology and Appl.27 (1987) 191-200. Zbl0641.46050MR911691
  19. 19 U. Seip, A convenient setting for differential calculus, J. Pure Appl. Algebra14 (1979) 73-100. Zbl0397.58014MR515488

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