Skip to main content
SpringerLink
Log in

Supercategories of Top and the Inevitable Emergence of Topological Constructs

  • Chapter
Handbook of the History of General Topology

Part of the book series: History of Topology ((HIPO,volume 3))

Abstract

Before embarking on our journey let us point out what we will not be doing, thereby stifling unjustified “great expectations” in the bud.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adâmek, J., Theory of Mathematical Structures, Reidel 1983.

    Google Scholar 

  2. Adâmek, J., Classification of concrete categories, Houston J. Math. 12 (1986), 305–326.

    Google Scholar 

  3. Adâmek, J. and Herrlich, H., Cartesian closed categories, quasitopoi and topological universes, Comment. Math. Univ. Carolinae 27 (1986), 235–257.

    MATH  Google Scholar 

  4. Adâmek, J., Herrlich, H. and Strecker, G.E., Least and largest initial completions, Comment. Math. Univ. Carolinae 20 (1979), 43–77.

    MATH  Google Scholar 

  5. Adâmek, J., Herrlich, H. and Strecker, G.E., The structure of initial completions, Cahiers Top. Géom. Diff. Categ. 20 (1979), 333–352.

    MATH  Google Scholar 

  6. Adâmek, J., Herrlich, H. and Strecker, G.E., Abstract and Concrete Categories, John Wiley 1990.

    Google Scholar 

  7. Adâmek, J. and Koubek, V., What to embed into a cartesian closed topological category, Comment. Math. Univ. Carolinae 18 (1977), 817–821.

    MathSciNet  MATH  Google Scholar 

  8. Adâmek, J. and Koubek, V., Cartesian closed functor-structured categories, Comment. Math. Univ. Carolinae 21 (1980), 573–589.

    MATH  Google Scholar 

  9. Adâmek, J. and Koubek, V., Cartesian closed initial completions, Topology Appl. 11 (1980), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  10. Adâmek, J. and Reiterman, J., Cartesian closed hull of the category of uniform spaces, Topology Appl. 19 (1987), 261–276.

    Article  Google Scholar 

  11. Adâmek, J., The quasitopos hull of the category of uniform spaces, Topology Appl. 27 (1987), 97–104.

    Article  MathSciNet  MATH  Google Scholar 

  12. Adâmek, J., Cartesian closed hull for metric spaces, Comment. Math. Univ. Carolinae 31 (1990), 1–6.

    MATH  Google Scholar 

  13. Adâmek, J., The quasitopos hull of the category of uniform spaces — a correction, Topology Appl. 48 (1992), 179–184.

    Article  MathSciNet  MATH  Google Scholar 

  14. Adâmek, J., Reiterman, J. and Schwartz, F., On universally topological hulls and quasitopos hulls, Houston J. Math. 17 (1991), 375–383.

    MathSciNet  MATH  Google Scholar 

  15. Adâmek, J., Reiterman, J. and Strecker, G.E., Realization of cartesian closed topological hulls, Manuscripta Math. 53 (1981), 1–33.

    Article  Google Scholar 

  16. Adâmek, J. and Strecker, G.E., Construction of cartesian closed topological hulls, Comment. Math. Univ. Carolinae 22 (1981), 235–254.

    MATH  Google Scholar 

  17. Alderton, I.W., Cartesian closedness and the Mac Neille completion of an initially structured category, Quaest. Math. 8 (1985), 63–78.

    Article  MathSciNet  MATH  Google Scholar 

  18. Alderton, I.W. and Schwarz, F., The extensional topological hull of the category of Cauchy spaces, Questions Answers Gen. Topol. 11 (1993), 193–198.

    MathSciNet  MATH  Google Scholar 

  19. Alderton, I.W., Cartesian closed extensions of the category of uniform spaces, Topology Appl. 75 (1994), 95–109.

    Article  MathSciNet  Google Scholar 

  20. Alderton, I.W., Schwarz, E and Weck-Schwarz, S., On the construction of the extensional topological hull, Cahiers Top. Géom. Diff. Categ. 35 (1994), 165174.

    Google Scholar 

  21. Aleksandrov, P.S. and Urysohn, P., Une condition nécessaire et suffisante pour qu’une classe (2) soit une classe (2), Compt. Rendus Acad. Sci. Paris 177 (1923), 1274–1277.

    Google Scholar 

  22. Antoine, P., Etude élémentaire des catégories d’ensembles structurés I, Bull. Soc. Math. Belgique 18 (1966), 142–164.

    MathSciNet  MATH  Google Scholar 

  23. Antoine, P., Etude élémentaire des catégories d’ensembles structurés II, Bull. Soc. Math. Belgique 18 (1966), 387–414.

    MathSciNet  MATH  Google Scholar 

  24. Antoine, P., Extension minimale de la catégorie des espaces topologiques, C. R. Acad. Sci. Paris 262 (1966), 1389–1392.

    MathSciNet  MATH  Google Scholar 

  25. Arens, R.F., A topology for spaces of transformations, Ann. Math. 47 (1946), 480–495.

    Article  MathSciNet  MATH  Google Scholar 

  26. Arhangel’skii, A.V. and Wiegandt, R., Connectedness and disconnectedness in topology, Topology Appl. 5 (1975), 9–33.

    Google Scholar 

  27. Aull, C.E. and Lowen, R. (eds.), Handbook of the History of General Topology, vol. 1. Kluwer Academic Publishers 1997.

    Google Scholar 

  28. Aull, C.E., (eds.), Handbook of the History of General Topology, vol. 2. Kluwer Academic Publishers 1998.

    Google Scholar 

  29. Balachandran, J., On the lattice of convergence topologies, J. Madras University 28 (1958), 129–146.

    Google Scholar 

  30. Banaschewski, B., A remark on extensions of Hausdorff spaces, Gen. Top. Appl. 4 (1974), 283–284.

    Article  MathSciNet  MATH  Google Scholar 

  31. Banaschewski, B., Essential extensions of To spaces, Gen. Top. Appl. 7 (1977), 233–246.

    MathSciNet  MATH  Google Scholar 

  32. Banaschewski, B. and Bruns, G., Categorical characterization of the MacNeille completion, Ann. of Math. 18 (1967), 369–377.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. Beattie, R. and Butzmann, H.-P., Convergence Structures in Functional Analysis, manuscript for a book, 2000.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  36. Bentley, H.L. and Herrlich, H., Extensions of topological spaces, in Proc. Memphis Top. Conf, 1976, 129–184.

    Google Scholar 

  37. Bentley, H.L. and Herrlich, H., Completion as reflection, Comment. Math. Univ. Carolinae 19 (1978), 541–568.

    MathSciNet  MATH  Google Scholar 

  38. Bentley, H.L., Herrlich, H. and Husek, M., The Historical Development of Uniform, Proximal and Nearness Concepts in Topology, Kluwer Academic Publishers 1998, 577–630.

    Google Scholar 

  39. Bentley, H.L., Herrlich, H. and Lowen, R., Improving constructions in topology, in Category Theory at Work, Heldermann Verlag 1991, 3–20.

    Google Scholar 

  40. Bentley, H.L., Herrlich, H. and Lowen-Colebunders, E., The category of Cauchy spaces is cartesian closed, Topology Appl. 27 (1987), 105–112.

    Article  MathSciNet  MATH  Google Scholar 

  41. Bentley, H.L., Herrlich, H. and Lowen-Colebunders, E., Convergence, J. Pure Appl. Algebra 68 (1990), 27–45.

    Article  MathSciNet  MATH  Google Scholar 

  42. Bentley, H.L., Herrlich, H. and Robertson, W.A., Convenient categories for topologists, Comment. Math. Univ. Carolinae 17 (1976) 207–227.

    MathSciNet  MATH  Google Scholar 

  43. Bentley, H.L. and Lowen-Colebunders, E., On the cartesian closed hull of the category of completely regular filter spaces, Cahiers Top. Géom. Diff. Categ. 33 (1992), 345–360.

    MathSciNet  MATH  Google Scholar 

  44. Bentley, H.L. and Naimpally, S.A., Wallmann Tl-compactifications as epireflections, Gen. Top. Appl. 4 (1974), 29–41.

    Article  MathSciNet  MATH  Google Scholar 

  45. Binz, E., Ein Differentierbarkeitsbegriff in limitierten Vektorräumen, Comment. Math. Helvetica 41 (1966), 137–156.

    Article  MathSciNet  MATH  Google Scholar 

  46. Binz, E., Bemerkungen zulimitierten Funktionenalgebren, Math. Ann. 175 (1968), 169–184.

    Article  MathSciNet  MATH  Google Scholar 

  47. Binz, E., Notes on a characterization of function algebras, Math. Ann. 186 (1970), 314–326.

    Article  MathSciNet  MATH  Google Scholar 

  48. Binz, E., Continuous convergence on C(X), vol. 469, Lecture Notes Math. Springer Verlag 1975.

    Google Scholar 

  49. Binz, E. and Keller, H.H., Kunktionenräume in der Kategorie der Limesräume, no. 383 in Ser. AI. Ann. Acad. Sci. Fennicae, 1966.

    Google Scholar 

  50. Birkhoff, G., Moore-Smith convergence in general topology, Ann. of Math. 38 (1937), 39–56.

    Article  MathSciNet  Google Scholar 

  51. Birkhoff, G., Lattice Theory, vol. XXV, Americam mathematical Society Colloquium Publications. AMS 1967.

    Google Scholar 

  52. Booth, P. and Tillotson, J., Monoidal closed, cartesian closed and convenient categories of topological spaces, Pacific J. Math. 88 (1980), 35–53.

    Article  MathSciNet  MATH  Google Scholar 

  53. Börger, R., Connectivity spaces and component categories, Heldermann Verlag 1984, 71–89.

    Google Scholar 

  54. Bourbaki, N., Topologie Générale, chapter 9, Utilisation des nombres réels en topologie générale, Hermann, Paris 1958.

    Google Scholar 

  55. Bourbaki, N., Topologie Générale, chapter 3, Groupes topologiques, 4. Nombres réels. Hermann, Paris 1960.

    Google Scholar 

  56. Bourbaki, N., Topologie Générale, chapter 5, Groupes a un paramètre, 6, Espaces numeriques et espaces projectifs, 7, Les groupes additifs Rn, 8, Nombres complexes. Hermann, Paris 1963.

    Google Scholar 

  57. Bourbaki, N., Topologie Générale, chapter 1, Structures topologiques, 2, Structures uniformes, Hermann, Paris 1965.

    Google Scholar 

  58. Bourbaki, N., Topologie Générale, chapter 10, Espaces fonctionnels. Hermann, Paris 1967.

    Google Scholar 

  59. Bourbaki, N., Théorie des Ensembles, Hermann, Paris 1970.

    MATH  Google Scholar 

  60. Bourdaud, G., Structures d’Antoine associées aux semi-topologies et aux topologies, Compt. Rendus Acad. Sci. Paris 279 (1974), 591–594.

    MathSciNet  MATH  Google Scholar 

  61. Bourdaud, G., Deux characterizations des c-espaces, Compt. Rendus Acad. Sci. Paris 281 (1975), 313–316.

    MathSciNet  MATH  Google Scholar 

  62. Bourdaud, G., Espaces d’Antoine et semi-espaces d’Antoine, Cahiers Top. Géom. Diff Categ. 16 (1975), 107–134.

    MathSciNet  MATH  Google Scholar 

  63. Bourdaud, G., Some cartesian closed topological categories of convergence spaces, Lecture Notes Math. 540 (1976), 93–108.

    Article  MathSciNet  Google Scholar 

  64. Brace, J.W., The topology of almost uniform convergence, Pac. J. Math. 9 (1959), 643–652.

    Article  MathSciNet  MATH  Google Scholar 

  65. Brandenburg, H. and Husek, M., A remark on cartesian closedness, in Category Theory, Proc. Gummersbach Conf. 1981, Springer-Verlag 1982, 33–38.

    Google Scholar 

  66. Brock, P. and Kent, D.C., Approach spaces, limit tower spaces and probabilistic convergence spaces, Applied Categ. Struct. 5 (1997), 99–110.

    Article  MathSciNet  MATH  Google Scholar 

  67. Brock, P. and Kent, D.C., On convergence approach spaces, Applied Categ. Struct. 6 (1998), 117–125.

    Google Scholar 

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

    Google Scholar 

  69. Brummer, G.C.L., Topological functors and structure functors, Lecture Notes Math. 540 (1976), 109–135.

    Article  MathSciNet  Google Scholar 

  70. Brummer, G.C.L., Topological categories, Topology Appl. 18 (1984), 27–41.

    Article  MathSciNet  Google Scholar 

  71. Brtimmer, G.C.L. and Giuli, E., A categorical concept of completion of objects, Comment. Math. Univ. Carolinae 33 (1992), 131–147.

    Google Scholar 

  72. BrUmmer, G.C.L. and Hoffmann, R.-E., An external characterization of topological functors, Lecture Notes Math. 540 (1976), 136–151.

    Article  MathSciNet  Google Scholar 

  73. Bruns, G., Die struktur der univerzweigten punktalen raumtypen, Math. Japonica 4 (1957), 123–132.

    MathSciNet  MATH  Google Scholar 

  74. Bruns, G. and Schmidt, J., Die puntalen typen topologischer räume, Math. Japonica 4 (1957), 133–177.

    Google Scholar 

  75. Burroni, A., T-categories, Cahiers Top. Géom. Diff. Categ. 12 (1971), 215–321.

    MathSciNet  MATH  Google Scholar 

  76. Butzmann, H.-P, Dualitäten in `ß (X), Ph.D. thesis, University of Mannheim, 1971.

    Google Scholar 

  77. Butzmann, H.-P., über die c-Reflexivität von Tc(X). Commentarii Math. Helvet. 47 (1972), 92–101.

    Google Scholar 

  78. Butzmann, H.-P., Der Satz von Stone-Weierstrass in `ß,(X) und seine Anwendungen auf die Darstellungstheorie von Limesalgebren, Habilitaion University of Mannheim 1974.

    Google Scholar 

  79. Butzmann, H.-P, and Kneis, G., Cech-stone compactifications of pseudotopological spaces, Math. Nachrichten 128 (1986) 259–264.

    Article  MathSciNet  MATH  Google Scholar 

  80. Cagliari, F., Disconnectednesses cogenerated by Hausdorff spaces, Cahiers Top. Géom. Diff. Categ. 29 (1985), 3–8.

    MathSciNet  Google Scholar 

  81. Cagliari, F. and Cicchese, M., Disconnectednesses and closure operators, Rend. Circ. Mat. Palermo 11 (1985), 15–23.

    MathSciNet  MATH  Google Scholar 

  82. Calenko, M.S., Functors between structured categories, Mat. Sb. 80 (1969), 533–552; Russian, Engl. transl. Math. USSR Sbornik 9, 497–513.

    Google Scholar 

  83. Caratheodory, C., Stetige Konvergenz und normale Familien von Funktionen, Math. Ann. 101 (1929), 515–533.

    Article  MathSciNet  MATH  Google Scholar 

  84. Cartan, H., Filtres et ultrafiltres, Compt. Rend. 205 (1937), 777–779.

    Google Scholar 

  85. Cartan, H., Théorie des filtres, Compt. Rend. 205 (1937), 595–598.

    Google Scholar 

  86. Ctech, E., Topological Spaces, Publishing House of the Czechoslovak Academy of Sciences, Interscience, John Wiley 1966.

    Google Scholar 

  87. Chittenden, E.W., On the equivalence of écart and voisinage, Trans. Amer. Math. Soc. 18 (1917), 161–166.

    MathSciNet  MATH  Google Scholar 

  88. Choquet, G., Convergences, Ann. Univ. de Grenoble 23 (1947), 57–112.

    MathSciNet  Google Scholar 

  89. Choquet, G., Convergences, Ann. Univ. Grenoble, Sect. Math. Phys. 23 (1948), 57–112.

    Google Scholar 

  90. Cincura, J., Closed structures on categories of topological spaces, Topology Appl. 20 (1985), 179–189.

    Article  MathSciNet  MATH  Google Scholar 

  91. Cincura, J., Cartesian closed coreflective subcategories of the category of topological spaces, Topology Appl. 41 (1991), 205–212.

    Google Scholar 

  92. Clementino, M.M., Hausdorff separation in categories, Applied Categ. Struct. 1 (1993), 285–296.

    Article  MathSciNet  MATH  Google Scholar 

  93. Clementino, M.M., On categorical notions of compact objects, Applied Categ. Struct. 4 (1996), 15–29.

    MathSciNet  MATH  Google Scholar 

  94. Clementino, M.M., Giuli, E. and Tholen, W., Topology in categories: compactness, Portugal. Math. 53 (1996), 397–433.

    MathSciNet  MATH  Google Scholar 

  95. Clementino, M.M. and Tholen, W., Separated and connected maps, Applied Categ. Struct. 6 (1998), 373–401.

    Article  MathSciNet  MATH  Google Scholar 

  96. Cochran, A.C. and Trail, R.B., Regularity and complete regularity for convergence spaces, in Proc. VPI Topology Conference, Springer Verlag 1973, 64–70.

    Google Scholar 

  97. Cogosvili, G.S., On convergence spaces, Math. Sb. 9 (1941), 377–381, Russian, German summary.

    Google Scholar 

  98. Cook, C.H., Compact pseudo-convergence, Math. Ann. 202 (1973), 193–202.

    Article  MathSciNet  MATH  Google Scholar 

  99. Cook, H.C. and Fisher, H.R., On equicontinuity and continuous convergence, Math. Ann. 159 (1965), 94–104.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  101. Csâszâr, A., Erweiterubg, Kompaktifizierung und Vervollständigung syntopogener Räume, in Proceedings Symposium Berlin 1967 on Extension Theory of Topological Structures, 1960, 51–54.

    Google Scholar 

  102. Csâszâr, A., Fondements de la Topologie Générale, Gauthiers-Villars, Paris 1960.

    MATH  Google Scholar 

  103. Csâszâr, A., Proximities, screens, merotopies, uniformities I, Acta. Math. Hung. 49 (1987), 459–479.

    Article  MATH  Google Scholar 

  104. Csâszâr, A., Proximities, screens, merotopies, uniformities II, Acta. Math. Hung. 50 (1987), 97–109.

    Article  Google Scholar 

  105. Csâszâr, A., Proximities, screens, merotopies, uniformities III, Acta. Math. Hung. 51 (1988), 23–33.

    Article  MATH  Google Scholar 

  106. Csâszâr, A., Proximities, screens, merotopies, uniformities IV, Acta. Math. Hung. 51 (1988), 151–164.

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  108. Day, B.J., Limit spaces and closed span categories, Lecture Notes Math. 420 (1974), 65–74.

    Article  Google Scholar 

  109. Day, B.J. and Kelly, G.M., On topological quotient maps preserved by pullbacks and products, Proc. Camb. Phil. Soc. 67 (1970), 553–558.

    Article  MathSciNet  MATH  Google Scholar 

  110. Deâk, J., A common topological supercategory for merotopies and syntopogenous structures, Colloq. Math. 55 (1993), 177–190.

    Google Scholar 

  111. DeMarr, R.E., Order convergence and topological convergence, Proc. Amer. Math. Soc. 16 (1965), 588–590.

    Article  MathSciNet  Google Scholar 

  112. Diers, Y., Categories of algebraic sets, Applied Categ. Struct. 4 (1996), 329–341.

    Article  MathSciNet  MATH  Google Scholar 

  113. Dikranjan, D. and Giuli, E., Closure operators, Topology Appl. 27 (1987), 129143.

    Google Scholar 

  114. Doicinov, D., A unified theory of topological, proximal and uniform spaces, Doklady Akad. Nauk SSSR 156 (1964), 21–24.

    MathSciNet  Google Scholar 

  115. Dolecki, S. and Greco, G.H., Cyrtologies of convergence I, Math. Nachrichten 126 (1986), 327–348.

    Article  MathSciNet  MATH  Google Scholar 

  116. Dolecki, S. and Greco, G.H., Cyrtologies of convergence II: sequential convergence, Math. Nachrichten 127 (1986), 317–334.

    Article  MathSciNet  MATH  Google Scholar 

  117. Dubuc, E.J., Concrete quasitopoi, Lecture Notes Math. 753 (1979), 239–254.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  119. Edgar, G.A., A cartesian closed category for topology, Gen. Top. Appl. 6 (1976), 65–72.

    Article  MathSciNet  MATH  Google Scholar 

  120. Efremovic, V.A., Nonequimorphism of the Euclidean and Lobacevski spaces (Russian). Uspekhi Mat. Nauk (4) 2 (1949), 178–179.

    MathSciNet  Google Scholar 

  121. Efremovic, V.A., Infinitesimal spaces (Russian), Doklady Akad. Nauk SSSR 76 (1951a.), 341–343.

    Google Scholar 

  122. Efremovic, V.A., Infinitesimal spaces (Russian), Mat. Sb. (6) 4 (195 lb), 203–204.

    Google Scholar 

  123. Efremovic, V.A., The geometry of proximity (Russian), Mat. Sb. 31 (1952), 189–200.

    MathSciNet  Google Scholar 

  124. Efremovic, V.A. and Svarc, A.S., A new definition of uniform spaces, Metrization of proximity spaces (Russian), Doklady Akad. Nauk SSSR 89 (1953), 393–396.

    MathSciNet  Google Scholar 

  125. Ehresmann, C., Structures quotient, Comment. Math. Helv. 38 (1964), 219–283.

    Article  MathSciNet  MATH  Google Scholar 

  126. Ehresmann, C., Catégories topologiques I, Indag. Math. 28 (1966), 133–146.

    MathSciNet  Google Scholar 

  127. Ehresmann, C., Catégories topologiques II, Indag. Math. 28 (1966), 147–160.

    MathSciNet  Google Scholar 

  128. Ehresmann, C., Catégories topologiques III, Indag. Math. 28 (1966), 161–175.

    MathSciNet  Google Scholar 

  129. Ehresmann, C., Catégories structurées généralisées, Cahiers Top. Géom. Diff. Categ. 10 (1968), 139–167.

    MathSciNet  Google Scholar 

  130. Fay, T.H., Brummer, G.C.L. and Hardie, K.A., A characterization of topological functors, Math. Coll. Univ. Cape Town 12 (1979), 85–93.

    MathSciNet  Google Scholar 

  131. Feldman, W.A., Topological spaces and their associated convergence function algebras, Ph.D. thesis, Queen’s University Kingston, 1971.

    Google Scholar 

  132. Fischer, H R, Limesräume, Math. Ann. 137 (1959), 269–303.

    Article  MathSciNet  MATH  Google Scholar 

  133. Fréchet, M., Sur quelques points du calcul fonctionel, Rend. Circ. Mat. Palermo 22 (1906), 1–74.

    Article  MATH  Google Scholar 

  134. Fréchet, M., Sur les classes V normales, Trans. Amer. Math. Soc. 14 (1913), 320–324.

    Article  MathSciNet  MATH  Google Scholar 

  135. Fréchet, M., Relations entre les notions de limite et de distance, Trans. Amer. Math. Soc. 19 (1918), 53–65.

    Article  MathSciNet  MATH  Google Scholar 

  136. Fréchet, M., Sur la notion de voisinage dans les ensembles abstraits, Bull. Sci. Math. 42 (1918), 138–156.

    Google Scholar 

  137. Fréchet, M., Sur les ensembles abstraits, Annales Scientifiques de l’École Normale Supérieure 38 (1921), 314–388.

    Google Scholar 

  138. Fréchet, M., Prolongement des fonctionelles continues sur un ensemble abstrait, Bull. Sci. Math. 48 (1924), 171–183.

    Google Scholar 

  139. Fréchet, M., Les Espaces Abstraits, Gauthier—Villars, Paris 1928.

    MATH  Google Scholar 

  140. Fric, R. and Koutmlc, V., Sequential structures, Abh. Akad. Wiss. DDR 4 (1980), 37–56.

    Google Scholar 

  141. Frölicher, A., Kompakt erzeugte Räume und limesräume, Math. Zeitschr. 129 (1972), 57–63.

    Article  MATH  Google Scholar 

  142. Frölicher, A., Cartesian closed categories and analysis of smooth maps, in Categories in Continuum Physics, vol. 1174, Lecture Notes Math., 1986.

    Google Scholar 

  143. Frölicher, A. and Bucher, W., Calculus in vectorspaces without norm, vol. 30, Lecture Notes Math. Springer Verlag 1966.

    Google Scholar 

  144. Frölicher, A. and Kriegl, A., Linear Spaces and Differnetiation Theory, John Wiley and Sons 1988.

    Google Scholar 

  145. Gähler, W., A topological approach to structure theory, Math. Nachrichten 100 (1981), 93–144.

    Article  MATH  Google Scholar 

  146. Gähler, W., Generalized convergence groups, Math. Nachrichten 150 (1991), 219–261.

    Google Scholar 

  147. Gähler, W., Convergence structures-historical remarks and the monadic approach, Bremen Mathematik Arbeitspapiere 48 (1997), 171–193.

    Google Scholar 

  148. Gähler, W., Grundstrukturen der Analysis, vol 1,Akademie Verlag Berlin 77.

    Google Scholar 

  149. Gähler, W., Grundstrukturen der Analysis, vol II,Akademie Verlag Berlin 78.

    Google Scholar 

  150. Gazik, R.J., Regularity of Richardson’s compactification, Canad. J. Math. 6 (1974), 1289–1293.

    Google Scholar 

  151. De Giorgi, E., y-convergenza e g-convergenza, Boll. Un. Mat. Ital. 5 (1977), 213–220.

    Google Scholar 

  152. Greve, G., General construction of monoidal closed structures in topological, uniform and nearness spaces, in Category Theory, Proc. Gummersbach Conf. 1981, Springer-Verlag 1982, 100–114.

    Google Scholar 

  153. Grimeisen, G., Gefilterte summation von filtern und iterierte grenzprozesse I, Math. Ann. 141 (1960), 318–342.

    Article  MathSciNet  MATH  Google Scholar 

  154. Grimeisen, G., Gefilterte summation von filtern und iterierte grenzprozesse II, Math. Ann. 144 (1961), 386–417.

    Article  MathSciNet  MATH  Google Scholar 

  155. Grimeisen, G., Zur stufenhebung bei topologischen räumen, Math. Ann. 147 (1962), 223–231.

    Article  MathSciNet  Google Scholar 

  156. Grimeisen, G., Das produkt topologischer räume in einer theorie der limesräume, Math. Z 82 (1963), 361–378.

    Article  MathSciNet  MATH  Google Scholar 

  157. Hahn, H., Theorie der reellen Funktionen, Berlin 1921.

    Google Scholar 

  158. Hajek, D.W. and Mysior, A., On non-simplicity of topological categories, Lecture Notes Math. 719 (1979), 84–93.

    Article  MathSciNet  Google Scholar 

  159. Harbarth, K., Über die äquivalenz verschiedener axiomsysteme für limesräume, Math. Nachr. 17 (1959), 261–272.

    Article  MathSciNet  MATH  Google Scholar 

  160. Harvey, J.M., To-separation in topological categories, Quaest. Math. 2 (1977), 177–190.

    Article  MathSciNet  MATH  Google Scholar 

  161. Hausdorff, F., Grundzüge der Mengenlehre, Verlag von Veit & Comp., Leipzig 1914.

    MATH  Google Scholar 

  162. Hausdorff, F., Gestufte Räume, Fund. Math. 25 (1935), 486–502.

    Google Scholar 

  163. Hedrlín, Z., Pultr, A. and Trnkovâ, V., Concerning a categorical approach to topological and algebraic theories, in Proceedings 2nd Prague Topol. Symp., 1966, 176–181.

    Google Scholar 

  164. Heldermann, N.C., A remark on the embedding of RoTop into the category of nearness spaces, Colloq. Math. 1980, 607–623.

    Google Scholar 

  165. Heldermann, N.C., Coreflections induced by fine functors in topological categories, Quaest. Math. 5 (1982), 119–133.

    Article  MathSciNet  MATH  Google Scholar 

  166. Helmberg, G., On convergence classes of sets, Proc. Amer. Math. Soc. 13 (1962), 918–921.

    Article  MathSciNet  MATH  Google Scholar 

  167. Herrlich, H., E-kompakte räume, Math. Zeitschr. 96 (1967), 228–255.

    Article  MathSciNet  MATH  Google Scholar 

  168. Herrlich, H., Topologische Reflexionen und Coreflexionen, Springer Lect. Notes Math. vol. 78. Springer Verlag 1968.

    Google Scholar 

  169. Herrlich, H., Categorical topology, Gen. Top. Appl. 1 (1971), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  171. Herrlich, H., A concept of nearness, Gen. Top. Appl. 4 (1974), 191–212.

    Article  MathSciNet  MATH  Google Scholar 

  172. Herrlich, H., Topological functors, General Topology Appl. 4 (1974), 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  173. Herrlich, H., Topological structures, Math. Centre Tracts Amsterdam 52 (1974), 59–122.

    MathSciNet  Google Scholar 

  174. Herrlich, H., Initial completions, Math. Zeitschrift 150 (1976), 101–110.

    Article  MathSciNet  MATH  Google Scholar 

  175. Herrlich, H., Initial and final completions, Lecture Notes Math. 719 (1979), 137–149.

    Article  MathSciNet  Google Scholar 

  176. Herrlich, H., Categorical topology 1971–1981, in Proc. Fifth Prague Topol. Sympos. 1981, Heldermann Verlag 1982, 279–383.

    Google Scholar 

  177. Herrlich, H., Are there convenient subcategories of TOP? Topology Appl. 15 (1983), 263–271.

    Article  MathSciNet  MATH  Google Scholar 

  178. Herrlich, H., Universal topology, in Categorical Topology, Proc. Conf. Toledo 1983, Heldermann Verlag 1984, 223–281.

    Google Scholar 

  179. Herrlich, H.,Topologie I: Topologische Räume, Heldermann Verlag 1986.

    Google Scholar 

  180. Herrlich, H., Topological improvements of categories of structured sets, Topology Appl. 27 (1987), 145–155.

    Google Scholar 

  181. Herrlich, H., Hereditary topological constructs, in General topology and its relations to modern analysis and algebra VI, Heldermann Verlag 1988, 249–262.

    Google Scholar 

  182. Herrlich, H., On the representability of partial morphisms in Top and in related constructs, Lecture Notes Math. 1348 (1988), 144–153.

    MathSciNet  Google Scholar 

  183. Herrlich, H. and Binz, E. (eds.), Categorical Topology, vol. 540, Lecture Notes Math. Springer Verlag 1975.

    Google Scholar 

  184. Herrlich, H. and Husek, M., Categorical topology, in Recent Progress in General Topology, Elsevier Publishing Co. 1992, 369–403.

    Google Scholar 

  185. Herrlich, H. and Husek, M., Some open categorical problems in TOP, Applied Categ. Struct. 1 (1993), 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  186. Herrlich, H., Lowen-Colebunders, E. and Schwarz, F., Improving Top: PrTop and PsTop, in Category Theory at Work, Heldermann Verlag 1991, 21–34.

    Google Scholar 

  187. Herrlich, H. and Nel, L.D., Cartesian closed topological hulls, Proc. Amer. Math. Soc. 62 (1977), 215–222.

    Article  MathSciNet  MATH  Google Scholar 

  188. Herrlich, H. and Pietro, C. (eds.), The Complete Work of Graciela Salicrup, Sociedad Matematica Mexicana 1988.

    Google Scholar 

  189. Herrlich, H. and Preuß, G. (eds.), Categorical Topology, vol. 719, Lecture Notes Math. Springer Verlag 1979.

    Google Scholar 

  190. Herrlich, H. and Rajagopalan, M., The quasicategory of quasispaces is illegitimate, Ann. of Math. 40 (1983), 364–366.

    MathSciNet  MATH  Google Scholar 

  191. Herrlich, H., Salicrup, G. and Vazquez, R., Light factorization structures, Quaest. Math. 3 (1979), 189–213.

    Article  MathSciNet  MATH  Google Scholar 

  192. Herrlich, H. and Strecker, G.E., Coreflective subcategories, Trans. Amer. Math. Soc. 157 (1971), 205–226.

    Article  MathSciNet  MATH  Google Scholar 

  193. Coreflective subcategories in general topology, Fund. Math. 73 (1972), 199–218.

    Google Scholar 

  194. Herrlich, H. and Zhang, D., Categorical properties of probabilistic convergence spaces, Applied Categ. Struct. 6 (1998), 495–513.

    Article  MathSciNet  MATH  Google Scholar 

  195. Herrmann, R.A., A nonstandard approach to pseudotopological compactificadons, Notices Amer. Math. Soc. 26 (1979), Al21.

    Google Scholar 

  196. Hoffmann, R.-E., Die kategorielle Auffassung der Initial-und Finaltopologie, Ph.D. thesis, Universität Bochum, 1972.

    Google Scholar 

  197. Hoffmann, R.-E., (’8, At)-universally topological functors, Habilitationsschrift, University of Düsseldorf 1974.

    Google Scholar 

  198. Hoffmann, R.-E., Topological functors and factorization, Arch. Math. 26 (1975), 1–7.

    Article  MATH  Google Scholar 

  199. Hoffmann, R.-E., Note on universal topological completions, Cahiers Top. Géom. Diff. Categ. 20 (1979), 199–216.

    MATH  Google Scholar 

  200. Hogbe-Nlend, H., Théorie des bornologies, vol. 213, Lecture Notes in Math. Springer Verlag 1971.

    Google Scholar 

  201. Hong, S.S., Limit operators and reflective subcategories, Lecture Notes Math. 378 (1974), 219–227.

    Article  Google Scholar 

  202. Hong, Y.H., On initially structured functors, J. Korean Math. Soc. 14 (1978), 159–165.

    MATH  Google Scholar 

  203. Hunsaker, W.H. and Sharma, P.L., Proximity spaces and topological functors, Proc. Amer. Math. Soc. 45 (1974), 419–425.

    Article  MathSciNet  MATH  Google Scholar 

  204. Husek, M., Generalized proximity and uniform spaces I, Comment. Math. Univ. Carolinae 5 (1964), 247–266.

    MathSciNet  Google Scholar 

  205. Husek, M., Generalized proximity and uniform spaces II, Comment. Math. Univ. Carolinae 6 (1964), 119–139.

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  207. Husek, M., Categorical methods in topology, in Proc. Symp. Gen. Top. Appl. Prague, 1966, 190–194.

    Google Scholar 

  208. Husek, M., Remarks on reflections, Comment. Math. Univ. Carolinae 7 (1966), 249–259.

    MathSciNet  MATH  Google Scholar 

  209. Husek, M., Categorial connections between generalized proximity spaces and corn- pactifications, in Proceedings Symposium Berlin 1967 on Extension Theory of Topological Structures, 1967, 127–132.

    Google Scholar 

  210. Husek, M., Construction of special functors and its applications, Comment. Math. Univ. Carolinae 8 (1967), 555–566.

    MathSciNet  MATH  Google Scholar 

  211. Husek, M., Lattices of reflections and coreflections in continuous structures, Lect. Notes Math, Springer 540 (1976), 401 124.

    MathSciNet  Google Scholar 

  212. Husek, M., History and development of Hausdorff’s work in extension in metric spaces, Recent Development of Gen. Top. and its Appl., Intern. Conf in memory of F. Hausdorff (1868–1942), Berlin 1992, Akademie Verlag 1992, 160–169.

    Google Scholar 

  213. Husek, M. and Pumplün, D., Disconnectedness, Quaest. Math. 13 (1990), 449459.

    Google Scholar 

  214. Husek, M. and Tozzi, A., Generalized reflective cum coreflective classes in Top and Unif, Applied Categ. Struct. 4 (1996), 57–68.

    Article  MathSciNet  MATH  Google Scholar 

  215. Isbell, J.R., Some remarks concerning categories and subspaces, Canad. J. Math. 9 (1957), 563–577.

    Article  MathSciNet  MATH  Google Scholar 

  216. Isbell, J.R., Uniform Spaces, AMS Providence, RI, 1964.

    MATH  Google Scholar 

  217. Ivanova, V.M. and Ivanov, A.A., Contiguity spaces and bicompact extensions, Isvestia Akad. Nauk. SSSR 23 (1959), 613–634.

    MathSciNet  MATH  Google Scholar 

  218. Kannan, V., Reflexive cum coreflexive subcategories in topology, Math. Ann. 195 (1972), 1972.

    Google Scholar 

  219. Katétov, M., Measures in fully normal spaces, Fund. Math. 38 (1951), 73–84.

    MathSciNet  MATH  Google Scholar 

  220. Katétov, M., On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85–91.

    MathSciNet  MATH  Google Scholar 

  221. Katétov, M., On two results from general topology (Czech), Cas. pest. mat. 82 (1957), 367.

    Google Scholar 

  222. Katétov, M., Über die Berührungsräume, Wiss. Zeitschrift Humboldt Univ. Berlin, Math. Reihe 9 (1959), 685–691.

    Google Scholar 

  223. Katétov, M., Allgemeine Stetigkeitsstrukturen, in Proc. Int. Congr. Math. Stockholm, 1963, 473–479.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  225. Katétov, M., Convergence structures, in General Topology and its Relations to Mod- ern Analysis and Algebra II, Proceedings of the 2nd Prague Topol. Sympos. 1966, Academic Press 1967, 207–216.

    Google Scholar 

  226. Keller, H., Räume stetiger multilinearer Abbildungen als Limesräume, Math. Ann. 159 (1965), 259–270.

    Article  MathSciNet  MATH  Google Scholar 

  227. Keller, H., Die Limes-uniformisierbarkeit der Limesraüme, Math. Ann. 176 (1968), 334–341.

    Article  MathSciNet  MATH  Google Scholar 

  228. Keller, H., Differential calculus in locally convex spaces vol. 417, Lecture Notes Math. Springer Verlag 1974.

    Google Scholar 

  229. Kennison, J.F., Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303–315.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  231. Kent, D.C., On the order topology in a lattice, Illinois J. Math. 10 (1966), 588–590.

    MathSciNet  Google Scholar 

  232. Kent, D.C., Convergence quotient maps, Fund. Math. 65 (1969), 187–205.

    MathSciNet  Google Scholar 

  233. Kent, D.C. and Richardson, G.D., Compactifications of convergence spaces, Intern. J. Math. Math. Sci. 2 (1979), 345–368.

    Article  MathSciNet  MATH  Google Scholar 

  234. Khrennikov, A.U., Some applications of Keller’s convergence structure to the nonlinear functional analysis, Proc. Int. Conf Convergence Structures and Applic. II, 1983, 113–117.

    Google Scholar 

  235. Kowalsky, H.J., Beiträge zur topologischen algebra, Math. Nachrichten 11 (1954), 143–185.

    Article  MathSciNet  MATH  Google Scholar 

  236. Kowalsky, H.J., Limesräume und Komplettierung, Math. Nachrichten 12 (1954), 301–340.

    Google Scholar 

  237. Kowalsky, H.J., Topologische Räume, Birkhäuser Verlag 1961.

    Google Scholar 

  238. Kriegl, A., A cartesian closed extension of the category of smooth Banach spaces, Heldermann Verlag 1984, 323–336.

    Google Scholar 

  239. Kriegl, A., Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen, Monatsh. Math. 95 (1983), 287–309.

    Article  MathSciNet  MATH  Google Scholar 

  240. Kueera, L. and Pultr, A., On a mechanism of defining morphisms in concrete categories, Cahiers Top. Géom. Diff Categ. 13 (1972), 397–410.

    Google Scholar 

  241. Kumar, Vinod, On the largest Hausdorff compactification of a Hausdorff convergence space, Bull. Austral._ Math. Soc. 16 (1977), 189–197.

    Google Scholar 

  242. Kuratowski, C., Sur l’opération A de l’analysis situs, Fund. Math. 3 (1922), 182–199.

    MATH  Google Scholar 

  243. Kuratowski, C., Topologie, Warsaw 1933.

    Google Scholar 

  244. Lee, R., The category of uniform convergence spaces is cartesian closed, Bull. Austral. Math. Soc. 15 (1976), 461–465.

    Google Scholar 

  245. Rosalyn Lee, S, Function Spaces in the Category of Uniform Convergence Spaces, Ph.D. thesis, Carnegie Mellon 1978.

    Google Scholar 

  246. Lee, S.J. and Nel, L.D., Foundational isomorphisms in continuous differentiation theory, Applied Categ. Struct. 6 (1998), 127–135.

    Article  MathSciNet  MATH  Google Scholar 

  247. Lord, H., Facorizations and Disconnectedness, Akademie Verlag, Berlin 1992, 197–202.

    Google Scholar 

  248. Lord, H.,, Factorization, diagonal separation and disconnectedness, Topology Appl. 47 (1992), 83–96.

    Article  MathSciNet  MATH  Google Scholar 

  249. Lowen, E. and Lowen, R., A quasitopos containing CONV and MET as full subcategories, Intern. J. Math. Math. Sci. 11 (1988), 417–438.

    Article  MathSciNet  MATH  Google Scholar 

  250. Lowen, E. and Lowen, R., Topological quasitopos hulls of categories containing topological and metric objects, Cahiers Top. Géom. Diff. Categ. 30 (1989), 213–228.

    MathSciNet  MATH  Google Scholar 

  251. Lowen, E., Lowen, R. and Verbeeck, C., Exponential objects in the construct PRAP, Cahiers Top. Géom. Diff. Categ. 38 (1997), 259–276.

    MathSciNet  MATH  Google Scholar 

  252. Lowen, R., Kuratowski’s measure of noncompactness revisited, Quarterly J. Math. Oxford 39 (1988), 235–254.

    Article  MathSciNet  MATH  Google Scholar 

  253. Lowen, R., Approach Spaces: a common supercategory of TOP and MET, Math. Nachrichten 141 (1989), 183–226.

    Article  MathSciNet  MATH  Google Scholar 

  254. Lowen, R., Cantor-connectedness revisited, Comment. Math. Univ. Carolinae 33 (1992), 525–532.

    MathSciNet  MATH  Google Scholar 

  255. Lowen, R., Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press 1997.

    MATH  Google Scholar 

  256. Lowen, R. and Robeys, K., Compactifications of products of metric spaces and their relation to Smirnov and tech-Stone compactifications, Topology Appl. 55 (1994), 163–183.

    Article  MathSciNet  MATH  Google Scholar 

  257. Lowen,R. and Sioen, M., A small note on separation in AP. to appear.

    Google Scholar 

  258. Lowen-Colebunders, E., Uniformizable Cauchy spaces, Intern. J. Math. Math. Sci. 5 (1982), 513–527.

    Article  MathSciNet  MATH  Google Scholar 

  259. Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, Marcel Dekker, New York 1989.

    MATH  Google Scholar 

  260. Lowen-Colebunders, E., Lowen, R. and Nauwelaerts, M., The cartesian closed hull of the category of approach spaces, Cahiers. Top. Géom. Diff. Categ., to appear.

    Google Scholar 

  261. Lowen-Colebunders, E. and Sonck, G., Exponential objects and cartesian closedness in the construct Prtop, Applied Categ. Struct. 1 (1993), 345–360.

    Article  MathSciNet  MATH  Google Scholar 

  262. Lowen-Colebunders, E., On the largest coreflective cartesian closed subconstruct of Prtop, Applied Categ. Struct. 4 (1996), 69–79.

    MathSciNet  MATH  Google Scholar 

  263. Machado, A., Espaces d’Antoine et pseudo-topologies, Cahiers Top. Géom. Diff. Categ. 14 (1973), 309–327.

    MathSciNet  MATH  Google Scholar 

  264. Malan, S.W., Relational structures, Ph.D. thesis, Rand Afrikaans Univ. Johannesburg 1976.

    Google Scholar 

  265. Marinescu, G., Topologische und pseudotopologische Vektorräume, Ed. Acad. Rep. Pop. Romîne 1959.

    MATH  Google Scholar 

  266. Marinescu, G., Espaces Vectoriels Pseudotopologiques et Théorie des Distributions, Deutscher Verlag der Wissenschaften 1963.

    Google Scholar 

  267. Marny, T., On epireflective subcategories of topological categories, Topology Appl. 10 (1970), 175–181.

    MathSciNet  Google Scholar 

  268. Marny, T., Rechts-Bikategoriestrukturen in toplogischen Kategorien, Ph.D. thesis, Free University Berlin, 1973.

    Google Scholar 

  269. Marny, T., Limit-metrizability of limit spaces and uniform limit spaces, Lecture Notes Math. 719 (1979), 234–242.

    Article  MathSciNet  Google Scholar 

  270. Mathews, J.C. and Anderson, R.F., A comparison of two modes of order convergence, Proc. Amer. Math. Soc. 18 (1967), 100–104.

    Article  MathSciNet  MATH  Google Scholar 

  271. Menu, J. and Pultr, A., On categories determined by Poset-and Set-valued functors, Comment. Math. Univ. Carolinae 15 (1974), 665–678.

    MathSciNet  MATH  Google Scholar 

  272. Menu, J. and Pultr, A., Simply (co)reflective subcategories of the categories determined by Poset-valued functors, Comment. Math. Univ. Carolinae 16 (1975), 161–172.

    MathSciNet  MATH  Google Scholar 

  273. Min, K.C. and Nel, L.D., Newton’s method and Frobenius-Dieudonné theorem in nennormable analysis, Applied Categ. Struct. 5 (1997), 205–216.

    Article  MathSciNet  MATH  Google Scholar 

  274. Monadi, A. and Nel, L.D., Holomorphy in convergence spaces, Applied Categ. Struct. 1 (1993), 233–245.

    MathSciNet  MATH  Google Scholar 

  275. Moore, E.H. and Smith, H.L., A general theory of limits, Amer. J. Math. 44 (1922), 102–121.

    Article  MathSciNet  MATH  Google Scholar 

  276. Mrówka, S., On the convergence of nets of sets, Fund. Math. 45 (1958), 237246.

    Google Scholar 

  277. Mrowka, S. and Pervin, W. On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446–449.

    Article  MathSciNet  MATH  Google Scholar 

  278. Müller, B., Uber den c-Dual eines Limesvektorräumes, Ph.D. thesis, University of Mannheim 1972.

    Google Scholar 

  279. Dualitätstheorie für vektorunderverbände von `6 (x), Math. Nachrichten 69 (1975), 273–284.

    Google Scholar 

  280. Müller, G., Allgemeine Konvergenzbegriffe im topologischen Vereinen und Verbänden, Math. Ann. 139 (1959), 76–86.

    Article  MathSciNet  MATH  Google Scholar 

  281. Mulvey, C., A categorical characterization of compactness, J. London Math. Soc. 17 (1978), 429–436.

    Article  MathSciNet  Google Scholar 

  282. Krishna Murti, S.B., A set of axioms for topological algebra, J. Indian Math. Soc. 4 (1940), 116–119.

    MathSciNet  Google Scholar 

  283. Naimpally, S.A. and Warrack, B.D., Proximity spaces, Cambridge University Press 1970.

    Google Scholar 

  284. Nakagawa, R., Natural relations, separations and connections, Questions Answers Gen. Topol. 3 (1985), 28–46.

    MATH  Google Scholar 

  285. Nakagawa, R., Categorical topology. In K. Morita and J. Nagata (eds.), Topics in General Topology, North Holland 1989, 563–623.

    Google Scholar 

  286. Nauwelaerts, M., Cartesian closed hull of (quasi-)metric spaces revisited, to appear.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  288. Nel, L.D., Cartesian closed topological categories, Lecture Notes Math. 540 (1976), 439–451.

    Article  MathSciNet  Google Scholar 

  289. Nel, L.D., Cartesian closed coreflective hulls, Quaest. Math. 2 (1977), 269–283.

    Article  MathSciNet  MATH  Google Scholar 

  290. Nel, L.D., Topological universes and smooth Gelfand—Naimark duality, Contem- porary Math. 30 (1984), 244–276.

    Article  MathSciNet  Google Scholar 

  291. Nel, L.D., Infinite dimensional calculus allowing nonconvex domains with empty interior, Monatsh. Math. 110 (1990), 145–166.

    Article  MathSciNet  MATH  Google Scholar 

  292. Nel, L.D., Introduction to categorical methods I and II, Carleton-Ottawa Mathe- matical Lecture Notes Series 11, Carleton University 1991.

    Google Scholar 

  293. Nel, L.D., Introduction to categorical methods III, Carleton-Ottawa Mathematical Lecture Notes Series 12, Carleton University 1991.

    Google Scholar 

  294. Nel, L.D., Differential calculus founded on an isomorphism, Applied Categ. Struct. 1 (1993), 51–57.

    Article  MathSciNet  MATH  Google Scholar 

  295. Ordman, E.T., Convergence almost everywhere is not topological, Amer. Math. Monthly 73 (1966), 1966.

    Google Scholar 

  296. Penon, J., Quasi-topos, C. R. Acad. Sci. Paris, Sér. A 276 (1973), 237–240.

    MathSciNet  MATH  Google Scholar 

  297. Penon, J., Sur les quasi-topos, Cahiers Top. Géom. Diff. Categ. 18 (1977), 181–218.

    MathSciNet  MATH  Google Scholar 

  298. Poppe, H., Stetige Konvergenz und der Satz von Ascoli und Arzelà, Math. Nachrichten 30 (1965), 87–122.

    Article  MathSciNet  MATH  Google Scholar 

  299. Poppe, H., Compactness in general function spaces, Deutscher Verlag der Wis- senschaften, Berlin 1974.

    MATH  Google Scholar 

  300. Porst, H.-E., Characterizations of MacNeille completions and topological functors, Bulletin Amer. Math. Soc. 18 (1978), 201–210.

    Article  MathSciNet  MATH  Google Scholar 

  301. Preuß, G., Trennung und Zusammenhang, Monatshefte fir Mathematik 74 (1970), 70–87.

    Article  MATH  Google Scholar 

  302. Preuß, G., Allgemeine Topologie, Hochschultext, Springer-Verlag 1972.

    Book  MATH  Google Scholar 

  303. Preuß, G., Relative connectednesses and disconnectednesses in topological cate- gories, Quaest. Math. 2 (1977), 297–306.

    Article  Google Scholar 

  304. Preuß, G., Connection properties in topological categories and related topics, Lecture Notes Math. 719 (1979), 293–307.

    Article  Google Scholar 

  305. Preuß, G., Connectednesses and disconnectednesses in S-near, in Categorical As- pects of Topology and Analysis, Proc. Ottawa Conf. 1980, Springer-Verlag 1982, 275–292.

    Google Scholar 

  306. Preuß, G., Theory of Topological Structures. Reidel, Dordrecht 1988.

    Book  MATH  Google Scholar 

  307. Preuß, G., Point Separation Axioms, Monotopological Categories and MacNeille Completions, Heldermann Verlag Berlin 1991, 47–55.

    Google Scholar 

  308. Preuß, G., Semiuiform limit spaces and semi-Cauchy spaces, in G. Preuß W. Gäh- ler, H. Herrlich (eds.), Recent Developments of General Topology and its Applications, Akademie Verlag 1992, 268–278.

    Google Scholar 

  309. Pultr, A., On full embeddings of concrete categories with respect to forgetful functors, Comment. Math. Univ. Carolinae 9 (1968), 281–305.

    MathSciNet  MATH  Google Scholar 

  310. Pultr, A. and Tozzi, A., Separation axioms and frame representations of some topological facts, Applied Categ. Struct. 2 (1994), 107–118.

    Article  MathSciNet  MATH  Google Scholar 

  311. Ramaley, J.F. and Wyler, O., Cauchy spaces: regular completions and compactifications, Math. Ann. 187 (1970), 187–199.

    Article  MathSciNet  MATH  Google Scholar 

  312. Ramaley, J.F. and Wyler, O., Cauchy spaces: structure and uniformization theorems, Math. Ann. 187 (1970), 175–186.

    Article  MathSciNet  MATH  Google Scholar 

  313. Rao, C.J.M., On smallest compactification for convergence spaces, Proc. Amer. Math. Soc. 44 (1974), 225–230.

    Article  MathSciNet  MATH  Google Scholar 

  314. Rao, C.J.M., On largest Hausdorff compactification for convergence spaces, Bull. Austral. Math. Soc. 12 (1975), 73–79.

    Article  MathSciNet  MATH  Google Scholar 

  315. Rennie, B.C., Lattices, Proc. Lond. Math, Soc. 52 (1951), 386–400.

    MathSciNet  MATH  Google Scholar 

  316. Richardson, G.D., A stone—tech compactification for limit spaces, Proc. Amer. Math. Soc. 25 (1970), 403–404.

    MathSciNet  MATH  Google Scholar 

  317. Richardson, G.D. and Kent, D.C., Regular compactifications of convergence spaces, Proc. Amer. Math. Soc. 31 (1972), 571–573.

    Article  MathSciNet  MATH  Google Scholar 

  318. Richter, G., More on exponential objects in categories of pretopological spaces, Applied Categ. Struct. 5 (1997), 309–319.

    MATH  Google Scholar 

  319. Riesz, F., Die Genesis des Raumbegriffs, Math. Naturwiss. Berichte Ungarn 24 (1906), 309–353.

    Google Scholar 

  320. Riesz, F., Stetigkeitsbegriff and abstrakte Mengenlehre, Atti del IV Congresso Intern. Matem., Roma 1908, II, Roma 1909, 18–24.

    Google Scholar 

  321. Roberts, J.E., A characterization of initial functors, J. Algebra 8 (1968), 181193.

    Google Scholar 

  322. Robertson, W., Convergence as a nearness concept, Ph.D. thesis, University of Ottawa at Carleton, 1975.

    Google Scholar 

  323. Rosickÿ, J., Model theoretic approach to topological functors I, 6th Winter School Abstract Anal.

    Google Scholar 

  324. Rosickÿ, J., Model theoretic approach to topological functors II, 7th Winter School Abstract Anal.

    Google Scholar 

  325. Rosinger, E., Pseudotopological structures, Acad. R. R Romine Stud. Cerc. Mat. 14 (1963), 223–251. Romanian, Russian and French summaries.

    Google Scholar 

  326. Salicrup, G. and Vazquez, R., Categorias de conexion, Anales d’Instituto de Mathematicas, 12 (1972), 47–87. English translation in “The Complete Work of Graciela Salicrup”, edited by H. Herrlich and C. Prieto, Sociedad Matematica Mexicana, 1988.

    Google Scholar 

  327. Salicrup, G., Connection and disconnection, Lecture Notes Math. 719 (1978), 326–244.

    Google Scholar 

  328. Schroder, M., Continuous convergence in a Gelfand theory for topological algebras, Ph.D. thesis, Queen’s University Kingston, 1971.

    Google Scholar 

  329. Schroder, M., Solid convergence spaces, Bull. Austral. Math. Soc. 8 (1973), 443–459.

    Article  MathSciNet  MATH  Google Scholar 

  330. Schwarz, E., Cartesian closedness, exponentiality, and final hulls in pseudotopological spaces, Quaest. Math. 5 (1982), 289–304.

    Article  MATH  Google Scholar 

  331. Schwarz, E., Exponential objects in categories of (pre)topological spaces and their natural function spaces. C. R. Math. Rep. Acad. Sci. Canada, IV, 6 (1982), 321–326.

    Google Scholar 

  332. Schwarz, E., Powers and exponential objects in initially structured categories and applications to categories of limit spaces, Quaest. Math. 6 (1983), 227–254.

    Article  MATH  Google Scholar 

  333. Schwarz, E., Hereditary topological categories and topological universes, Quaest. Math. 10 (1986), 197–216.

    Article  MATH  Google Scholar 

  334. Schwarz, E., Description of the topological universe hull, Lect. Notes in Comp. Sci. 393 (1989), 325–332.

    Article  Google Scholar 

  335. Schwarz, F. and Weck, S., Internal description of hulls: a unifying approach, in Category theory at work. Heldermann Verlag 1991.

    Google Scholar 

  336. Schwarz, E and Weck-Schwarz, S., On hereditary and product-stable quotient maps, Comment. Math. Univ. Caroline 33 (1992), 345–352.

    MathSciNet  MATH  Google Scholar 

  337. Seip, U., Differential calculus and cartesian closedness, in Categorical Topology, vol. 540, Lecture Notes Math., Springer Verlag 1975, 578–604.

    Chapter  Google Scholar 

  338. Semadeni, Z., Projectivity, injectivity and duality, Rozprawy Mat., 1963, p. 35.

    Google Scholar 

  339. Smirnov, J.M., On proximity spaces in the sense of V. A. Efremovic (Russian). Doklady Akad. Nauk SSSR 84 (1952a), 895–898.

    MathSciNet  MATH  Google Scholar 

  340. Smirnov, J.M., On proximity spaces (Russian), Mat. Sb. 31 (1952b), 543–574.

    Google Scholar 

  341. Smirnov, J.M., On completeness of proximity spaces (Russian), Doklady Akad. Nauk SSSR 88 (1953a), 761–764.

    MathSciNet  MATH  Google Scholar 

  342. Smirnov, J.M., On completeness of of uniform and proximity spaces (Russian), Doklady Akad. Nauk SSSR 91 (1953b), 1281–1284.

    MathSciNet  MATH  Google Scholar 

  343. Smirnov, J.M., On completeness of proximity spaces (Russian), Trudy Mosk. Mat. Obséestva 3 (1954), 271–306.

    MATH  Google Scholar 

  344. Smirnov, J.M., On completeness of proximity spaces, II (Russian), Trudy Mosk. Mat. Obséestva 4 (1955), 421–438.

    MATH  Google Scholar 

  345. Sonner, H., Die Polarität zwischen topologischen räumen und limesräume, Ann. of Math. 4 (1953), 461–469.

    MathSciNet  MATH  Google Scholar 

  346. Sonner, J., Canonical categories, in Proc. Conf. La Jolla 1965 on Categorical Algebra, 1965, 272–294.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  348. Steenrod, N.E., A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133–152.

    Article  MathSciNet  MATH  Google Scholar 

  349. Strecker, G.E., On cartesian closed topological hulls, in Categorical Topology, Heldermann Verlag 1984.

    Google Scholar 

  350. Szymanski, P., La notion des ensembles séparés comme terme primitif de la topologie, Math. Timisoara 17 (1941), 65–84.

    MathSciNet  Google Scholar 

  351. Taylor, J.C., Weak families of maps, Canad. Math. Bull. 8 (1965), 771–781.

    Article  MathSciNet  MATH  Google Scholar 

  352. Tholen, W., Reflective subcategories, Topology Appl. 27 (1987), 201–212.

    Article  MathSciNet  MATH  Google Scholar 

  353. Titcomb, T., Fibers of relatively topological functors, Ph.D. thesis, Kansas State University, 1980.

    Google Scholar 

  354. Tozzi, A. and Wyler, O., On categories of supertopological spaces, Acta Univ. Carolinae Math. et Phys. 28 (1987), 137–149.

    MathSciNet  MATH  Google Scholar 

  355. Urysohn, P., Über die Mächtigkeit der zusammenhängenden mengen, Math. Ann. 94 (1925), 309–315.

    Article  MathSciNet  MATH  Google Scholar 

  356. Urysohn, P., Zum metrisationproblem, Math. Ann. 94 (1925), 262–295.

    Article  MathSciNet  MATH  Google Scholar 

  357. Urysohn, P., Sur les classes L de M. Fréchet, Ens. Math. 25 (1926), 77–83.

    MATH  Google Scholar 

  358. Vaino, R., On Connectedness in Limit Space Theory, Akademie Verlag Berlin 1984, 227–232.

    Google Scholar 

  359. Vilímovsk, J., Generations of coreflections in categories, Comment. Math. Univ. Carolinae, 14 (1973), 305–323.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  361. Wagner, E., On the convergence structure of Mikusinski operators, Studia Math. 27 (1966), 39–48.

    MathSciNet  MATH  Google Scholar 

  362. Wallace, A.D., Separation spaces, Annals of Math. 42 (1942), 687–697.

    Article  Google Scholar 

  363. Ward, A.J., On relations between certain intrinsic topologies in partially ordered sets, Proc. Cambridge Philos. Soc. 51 (1955), 254–261.

    Article  MathSciNet  MATH  Google Scholar 

  364. Weck-Schwarz, S., Cartesian closed topological and monotopological hulls: A comparison, Topology Appl. 38 (1991), 263–274.

    Article  MathSciNet  MATH  Google Scholar 

  365. Weck-Schwarz, S., To—objects and separated objects in topological categories, Quaest. Math. 14 (1991), 315–325.

    Article  MathSciNet  MATH  Google Scholar 

  366. Weil, A., Les recouvrements des espaces topologiques: espaces complets, espaces bicompacts. Compt. Rendus Acad. Sci. Paris 202 (1936), 1002–1005.

    Google Scholar 

  367. Weil, A., Sur les espaces à structure uniforme et sur la topologie générale, Actual. Sci. Ind., 1937, p. 551.

    Google Scholar 

  368. Wischnewsky, M.B., Initialkategorien, Ph.D. thesis, University of Munchen, 1972.

    Google Scholar 

  369. Weil, A., Aspects of universal algebra in initialstructure categories, Cahiers Top. Géom. Diff. Categ. 14 (1974), 1–27.

    Google Scholar 

  370. Wloka, J., Limesräume und distributionen, Math. Ann. 152 (1963), 351–409.

    MathSciNet  MATH  Google Scholar 

  371. Wolff, H., On the external characterization of topological functors, Manuscripta Math. 22 (1977), 63–76.

    Article  MathSciNet  MATH  Google Scholar 

  372. Wyler, O., The Stone-tech compactification for limit spaces, Notices Amer. Math. Soc. 15 (1968), 169.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  374. Wyler, O., Top categories and categorical topology, General Topology Appl. 1 (1971), 17–28.

    Google Scholar 

  375. Wyler, O., Are there topoi in topology? in Categorical Topology, E. Binz and H. Herrlich (eds.), Springer Verlag 1976, 699–719.

    Google Scholar 

  376. Wyler, O., Function spaces in topological categories, Lecture Notes Math. 719 (1979), 411–420.

    Article  MathSciNet  Google Scholar 

  377. Wyler, O., On convergence of filters and ultrafilters to subsets, in Categorical meth- ods in computer science, H. Ehrig, H. Herrlich, H.J. Kreowski, and G. Preuß (eds.), Springer Verlag 1989, 340–350.

    Google Scholar 

  378. Wyler, O., Lecture Notes on Topoi and Quasitopoi, World Scientific 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departement Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    E. Lowen-Colebunders

  2. Departement Wiskunde en Informatica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020, Antwerp, Belgium

    R. Lowen

Authors
  1. E. Lowen-Colebunders
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Lowen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    C. E. Aull

  2. Department of Mathematics and Computer Science, University of Antwerp, RUCA, Antwerp, Belgium

    R. Lowen

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Lowen-Colebunders, E., Lowen, R. (2001). Supercategories of Top and the Inevitable Emergence of Topological Constructs. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0470-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0470-0_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5704-4

  • Online ISBN: 978-94-017-0470-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation