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Cartesian closed topological categories

Part of the Lecture Notes in Mathematics book series (LNM,volume 540)

Keywords

  • Topological Space
  • Compact Hausdorff Space
  • Finite Product
  • Topological Algebra
  • Springer Lecture Note

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Bibliography

  1. P. Antoine, Etude élémentaire des categories d'ensembles structurés, Bull. Soc. Math. Belge 18 (1966) 142–164 and 387–414.

    MathSciNet  MATH  Google Scholar 

  2. P. Antoine, Notion de compacité et quasi-topologie, Cahiers de Top. et Geom. Diff. 14 (1973) 291–308.

    MathSciNet  MATH  Google Scholar 

  3. A. Bastiani, Applications differentiables et varietés differentiables de dimension infinie, J. Analyse Math. 13 (1964) 1–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. H.L. Bentley, T-categories and some representation theorems, Portugaliae Math. 32 (1973) 201–222.

    MathSciNet  MATH  Google Scholar 

  5. H.L. Bentley, H. Herrlich and W.A. Robertson, Convenient categories for topologists, Comm. Math. Univ. Carolinae (to appear).

    Google Scholar 

  6. E. Binz, Bemerkungen zu limitierten Funktionenalgebren, Math. Ann 175 (1968) 169–184.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. E. Binz, Continuous Convergence on C(X), Springer Lecture Notes in Math. 469 (1975).

    Google Scholar 

  8. E. Binz and H.H. Keller, Funktionenraume in der Kategorie der Limesraume, Ann. Acad. Sci. Fenn. Sec. AI 383 (1966) 1–21.

    MathSciNet  MATH  Google Scholar 

  9. N. Bourbaki, Topologie Générale, Hermann et cie, Paris (1948).

    MATH  Google Scholar 

  10. G. Bourdaud, Structure d'Antoine associées aux semi-topologies et aux topologies, C.R. Acad. Sci. Paris Ser. A279 (1974) 591–594.

    MathSciNet  MATH  Google Scholar 

  11. H. Breger, Die Kategorie der kompakt-erzeugten Raume als in Top coreflective Kategorie mit Exponentialgesetz, Diplomarbeit, Univ. Heidelberg (1971).

    Google Scholar 

  12. R. Brown, Function spaces and product topologies, Quart. J. Math. Oxford 15 (1964) 238–250.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. G.C.L. Brummer, A categorical study of initiality in uniform topology, Ph.D. thesis, Univ. Cape Town 1971.

    Google Scholar 

  14. C.H. Cook and H.R. Fischer, On equicontinuity and uniform convergence, Math. Ann. 159 (1965) 94–104.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. C.H. Cook and H.R. Fischer, Uniform convergence structures, Math. Ann. 173 (1967) 290–306.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. G. Choquet, Convergences, Ann. Univ. Grenoble (i.e. Ann. Inst. Fourier) 23 (1947/48) 57–112.

    MathSciNet  MATH  Google Scholar 

  17. D. Damerov, Die Kategorie der Kelley-Raume, Diplomarbeit, Freie Univ. Berlin (1969).

    Google Scholar 

  18. B. Day, A reflection theorm for closed categories, J. Pure Appl. Algebra 2 (1972) 1–11.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. B. Day, An embedding theorem for closed categories, Category Seminar, Sydney (1972/73) Springer Lecture Notes in Math. 420 (1974).

    Google Scholar 

  20. E.J. Dubuc and H. Porta, Convenient categories of topological algebras and their duality theory, J. Pure Appl. Algebra 1 (1971) 281–316.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. S. Eilenberg and G.M. Kelly, Closed categories, Proc. Conf. on Categorical Algebra, La Jolla (1965) Springer, Berlin (1966) 421–562.

    MATH  Google Scholar 

  22. H.R. Fischer, Limesraume, Math. Ann 137 (1959) 269–303.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. D. Franke, Funktionenalgebren in cartesisch abgeschlossenen Kategorien, Thesis, Free Univ. Berlin (1975).

    Google Scholar 

  24. A. Frolicher and W. Bucher, Calculus in vector spaces without norm, Springer Lecture Notes in Math. 30 (1966).

    Google Scholar 

  25. K.A. Hardie, Derived homotopy constructions, J. London Math. Soc. 35 (1960) 465–480.

    MathSciNet  MATH  Google Scholar 

  26. H. Herrlich, Topological functors, Gen. Top. Appl. 4 (1974) 125–142.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. H. Herrlich, Topological structures, Math. Centre Tract 25 (1974) 59–122.

    MathSciNet  MATH  Google Scholar 

  28. H. Herrlich, Cartesian closed topological categories, Math. Colloq. Univ. Cape Town 9 (1974) 1–16.

    MathSciNet  MATH  Google Scholar 

  29. H. Herrlich and G. E. Strecker, Category Theory, Allyn and Bacon, Boston (1973).

    MATH  Google Scholar 

  30. R. E. Hoffmann, Topological functors and factorizations (preprint)

    Google Scholar 

  31. R.E. Hoffmann, (E,M)-universally topological functors (preprint)

    Google Scholar 

  32. H. Hogbe-Nlend, Theorie des bornologies et applications, Springer Lecture Notes in Math. 213 (1971).

    Google Scholar 

  33. W. N. Hunsaker and P. L. Sharma, Proximity spaces and topological functors, Proc. Amer. Math. Soc.

    Google Scholar 

  34. M. Husek, S-categories, Comment. Math. Univ. Caroliniae 5 (1964) 37–46.

    MathSciNet  MATH  Google Scholar 

  35. M. Husek, Categorical methods in topology, Proc. Symp. Gen. Topol. Appl. Prague (1966) 190–194.

    Google Scholar 

  36. M. Husek, Construction of special functors and its applications, Comment. Math. Univ. Carolinae 8 (1967) 555–556.

    MathSciNet  MATH  Google Scholar 

  37. S.H. Kamnitzer, Protoreflections, relational algebras and topology, Thesis, Univ. Cape Town (1974).

    Google Scholar 

  38. J. Isbell, Adequate subcategories, Illinois J. Math. 4 (1960) 541–552.

    MathSciNet  MATH  Google Scholar 

  39. M. Katetov, On continuity structures and spaces of mappings, Comment. Math. Univ. Carolinae 6 (1965) 257–278.

    MathSciNet  MATH  Google Scholar 

  40. H. Keller, Differential Calculus in Locally Convex Spaces, Springer Lecture Notes in Math. 417 (1974).

    Google Scholar 

  41. D. C. Kent, Convergence functions and their related toplogies, Fund. Math. 54 (1964) 125–133.

    MathSciNet  MATH  Google Scholar 

  42. D.C. Kent, On convergence groups and convergence uniformities, Fund. Math. 60 (1967) 213–222.

    MathSciNet  MATH  Google Scholar 

  43. D. C. Kent and G. D. Richartdson, Locally compact convergence spaces (preprint)

    Google Scholar 

  44. H.J. Kowalsky, Limesraume und Komplettierrung, Math. Nachr. 12 (1954) 301–340.

    CrossRef  MathSciNet  MATH  Google Scholar 

  45. W.F. LaMartin, k-groups, Thesis, Tulane Univ. (1973).

    Google Scholar 

  46. A. Machado, Quasi-variétés complexed, Cahiers de Top. et Geom. Diff. 11 (1970) 231–279.

    Google Scholar 

  47. A. Machado, Espaces d'Antoine et pseudo-topologies, Cahiers de Top. et Geom. Diff. 14 (1973) 309–327.

    MathSciNet  MATH  Google Scholar 

  48. S. MacLane, Categories for the Working Mathematician, Springer, New York (1971).

    MATH  Google Scholar 

  49. L.D. Nel, Initially structured categories and cartesian closedness, Canad. J. Math. 27 (1975) 1361–1377.

    CrossRef  MathSciNet  MATH  Google Scholar 

  50. H. Poppe, Compactness in general function spaces, VEB Deutscher Verlag der Wissenschaften, Berlin (1974).

    MATH  Google Scholar 

  51. R. Pupier, Precompactologie et structures uniformes, Fund. Math. 83 (1974) 251–262.

    MathSciNet  MATH  Google Scholar 

  52. W. A. Robertson, Convergence as a nearness concept, Thesis, Carleton Univ. (1975).

    Google Scholar 

  53. U. Seip, Kompakt erzeugte Vektorraume und Analysis, Springer Lecture Notes in Math. 273 (1972).

    Google Scholar 

  54. E. Spanier, Quasi-topologies, Duke Math. J. 30 (1963) 1–14.

    CrossRef  MathSciNet  MATH  Google Scholar 

  55. N.E. Steenrod, Aconvenient category of topological spaces, Michigan Math. J. 14 (1967) 133–152.

    CrossRef  MathSciNet  MATH  Google Scholar 

  56. R.M. Vogt, Convenient categories of topological spaces for homotopy theory, Archiv. Math. 22 (1971) 545–555.

    CrossRef  MathSciNet  MATH  Google Scholar 

  57. M. Wischnewsky, Partielle Algebren in Initial-kategorien, Math. Zeitschr. 127 (1972) 17–28.

    CrossRef  MathSciNet  MATH  Google Scholar 

  58. M. Wischnewsky, Generalized universal algebra in initialstructure categories, Algebra-Berichte (Uni-Druck, Munchen) 10 (1973) 1–35.

    MATH  Google Scholar 

  59. O. Wyler, On the categories of general topology and topological algebra, Archiv. Math. 22 (1971) 7–17.

    CrossRef  MathSciNet  MATH  Google Scholar 

  60. O. Wyler, TOP Categories and categorical topology, Gen. Topol. Appl. 1 (1971) 17–28.

    CrossRef  MathSciNet  MATH  Google Scholar 

  61. O. Wyler, Convenient categories for topology, Gen. Topol. Appl. 3 (1973) 225–242.

    CrossRef  MathSciNet  MATH  Google Scholar 

Closely related talks given at this conference

  1. G. Bourdaud, Some closed topological categories of convergence spaces.

    Google Scholar 

  2. H. Herrlich, Some topological theorems which fail to be true.

    Google Scholar 

  3. W.A. Robertson, Cartesian closed categories of Nearness structures.

    Google Scholar 

  4. O. Wyler, Are there topoi in topology?

    Google Scholar 

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Nel, L.D. (1976). Cartesian closed topological categories. In: Binz, E., Herrlich, H. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080870

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  • DOI: https://doi.org/10.1007/BFb0080870

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