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Contributions and Importance of Professor George E. Strecker’s Research

  • Jürgen Koslowski
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

We give an overview of the long and distinguished career of Professor George E. Strecker in the fields of topology and, in particular, categorical topology.

Keywords

Category Theory General Topology Hausdorff Space Galois Connection Joint Paper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

George E. Strecker’s Topological Articles

  1. [vEBMvdS + 65]
    P. van Emde Boas, D. Mantel, J. van der Slot, George E. Strecker and E. Wattel. De onderlinge afhankelijkheid van een aantal topologische axioma’s die verband houden met het k-axioma (The underlying connections between topological axioms similar to the k-axiom). Technical Report ZW1965–018, Math. Centrum Amsterdam Afd. Zuivere Wisk., 1965.Google Scholar
  2. [SW66]
    George E. Strecker and E. Wattel. A coherent embedding of an arbitrary topological space in a semi-regular space. Technical Report ZW1966–006, Math. Centrum Amsterdam Afd. Zuivere Wisk., 1966. (Zbl. 148.43003, MR 39#923)MATHGoogle Scholar
  3. [Str66]
    George E. Strecker. On topologies congruent with their classes of dense sets. Technical Report ZW1966–019, Math. Centrum Amsterdam Afd. Zuivere Wisk., 1966.Google Scholar
  4. [SW67]
    George E. Strecker and E. Wattel. On semi-regular and minimal Hausdorff embeddings. Nederl. Akad. Wetensch. Indag. Math., (29):234–237, 1967. (Zbl. 148.43004/5, MR 35#2261)Google Scholar
  5. [dGSW67]
    Johannes de Groot, George E. Strecker, and E. Wattel. The compactness operator in general topology. In General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966), pages 161–163. Academia, Prague, 1967. (Zbl. 165.25301, MR 38#657)Google Scholar
  6. [SWHdG68]
    George E. Strecker, E. Wattel, Horst Herrlich, and Johannes de Groot. Strengthening Alexander’s subbase theorem. Duke Math. J., 35:671–676, 1968. (Zbl. 169.25001, MR 37#6912)MathSciNetMATHCrossRefGoogle Scholar
  7. [HS68]
    Horst Herrlich and George E. Strecker. H -closed spaces and reflective subcategories. Math. Ann., 177:302–309, 1968. (Zbl. 157.29104, MR 38#2744)MathSciNetMATHCrossRefGoogle Scholar
  8. [SV69]
    George E. Strecker and G. Viglino. Cotopology and minimal Hausdorff spaces. Proc. Amer. Math. Soc., 21:569–574, 1969. (Zbl. 175.49404, MR 39#2115)MathSciNetMATHCrossRefGoogle Scholar
  9. [dGHSW69]
    Johannes de Groot, Horst Herrlich, George E. Strecker, and E. Wattel. Compactness as an operator. Compositio Math., 21:349-375, 1969. (Zbl. 186.55902, MR 41#4490)MathSciNetMATHGoogle Scholar
  10. [LS72]
    C. T. Liu and George E. Strecker. Concerning almost realcompactifications. Czechoslovak Math. J., 22:181–190, 1972. (Zbl. 247.54024, MR 46#2644)MathSciNetGoogle Scholar
  11. [HS72a]
    D. W. Hajek and George E. Strecker. Direct limits of Hausdorff spaces. In General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971), pages 165–169, Prague, 1972. Academia. (Zbl. 306.54017, MR 50#8410)Google Scholar
  12. [DS73]
    F. A. Delahan and George E. Strecker. A simplified approach to the compactification of mappings. Bull. Amer. Math. Soc., 79:1030–1032, 1973. (Zbl. 268.54014, MR 47#7685)MathSciNetMATHCrossRefGoogle Scholar
  13. [DS77]
    F. A. Delahan and George E. Strecker. Graphic extensions of mappings. Quaestiones Math., 2:401–417, 1977. (Zbl. 365.54004, MR 58#2692)MathSciNetMATHCrossRefGoogle Scholar
  14. [HS97b]
    Horst Herrlich and George E. Strecker. When is N Lindelöf? Comment. Math. Univ. Carolinae, 38(3):553–556, 1997. (Zbl. 938.54008, MR 99f:99c:03070).MathSciNetMATHGoogle Scholar

George E. Strecker’s Categorical Articles

  1. [HS71a]
    Horst Herrlich and George E. Strecker. Coreflective subcategories. Trans. Amer. Math. Soc., 157:205–226, 1971. (Zbl. 224.18003, MR 43#6281)MathSciNetMATHCrossRefGoogle Scholar
  2. [HS71b]
    Horst Herrlich and George E. Strecker. Algebra ∩ topology = compactness. General Topology and Appl., 1:283–287, 1971. (Zbl. 231.18007, MR 46#7349)MathSciNetMATHCrossRefGoogle Scholar
  3. [HS72b]
    Horst Herrlich and George E. Strecker. Coreflective subcategories in general topology. Fund. Math., 73:199–218, 1972. (Zbl. 231.18008, MR 46#1872)MathSciNetMATHGoogle Scholar
  4. [Str72]
    George E. Strecker. Epireflection operators vs perfect morphisms and closed classes of epimorphisms. Bull. Austral. Math. Soc., 7:359–366, 1972. (Zbl. 2242.18004, MR 48#368)MathSciNetMATHCrossRefGoogle Scholar
  5. [Str74a]
    George E. Strecker. On characterizations of perfect morphisms and epireflective hulls. In TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), pages 468–500. Lecture Notes in Math., Vol. 378, Berlin — Heidelberg — New York, 1974. Springer-Verlag. (Zbl. 289.18004, MR 51#1709)Google Scholar
  6. [Str74b]
    George E. Strecker. Component properties and factorizations. In Topological structures (Proc. Sympos. in honour of Johannes de Groot (1914–1972), Amsterdam, 1973), number 52 in Math. Centre Tracts, pages 123–140, Amsterdam, 1974. Math. Centrum. (Zbl. 293.54010, MR 50#8421)Google Scholar
  7. [Str76]
    George E. Strecker. Perfect sources. In Categorical topology (Proc. Conf., Mannheim, 1975), pages 605–624. Lecture Notes in Math., Vol. 540, Berlin — Heidelberg — New York, 1976. Springer-Verlag. (Zbl. 338.54007, MR 56#9479)Google Scholar
  8. [HS79a]
    Horst Herrlich and George E. Strecker. Semi-universal maps and universal initial completions. Pacific J. Math., 82(2):407–428, 1979. (Zbl. 379.18008/414.18005, MR 81f:18005)MathSciNetMATHGoogle Scholar
  9. [AHS79a]
    Jiří Adamek, Horst Herrlich, and George E. Strecker. Least and largest initial completions. I. Comment. Math. Univ. Carolinae, 20:43–58, 1979. (Zbl. 404.18005, MR 80f: 18009)MathSciNetMATHGoogle Scholar
  10. [AHS79b]
    Jiří Adamek, Horst Herrlich, and George E. Strecker. Least and largest initial completions. II. Comment. Math. Univ. Carolinae, 20:59–77, 1979. (Zbl. 404.18006, MR 80f: 18009)MathSciNetMATHGoogle Scholar
  11. [AHS79c]
    Jiří Adámek, Horst Herrlich, and George E. Strecker. The structure of initial completions. Cahiers Topologie Géom. Différentielle, 20(4):333–352, 1979. (Zbl. 436.18001, MR 81d:18009)MATHGoogle Scholar
  12. [HS79b]
    Horst Herrlich and George E. Strecker. Algebra ⋃ topology. In Categorical topology (Proc. int. Conf., Berlin, 1978), volume 719 of Lecture Notes in Math., pages 150–156, Berlin — Heidelberg — New York, 1979. Springer-Verlag. (Zbl. 399.18003, MR 80j:18013)Google Scholar
  13. [HS79c]
    H. Herrlich and George E. Strecker. Semi-universal maps and universal initial completions. In Structure of topological categories (Proc. Conf., Univ. Bremen, Bremen, 1978), pages 75–108, Bremen, 1979. Univ. Bremen. (MR 82b:18004)Google Scholar
  14. [HNST80]
    Horst Herrlich, R. Nakagawa, George E. Strecker, and Tim Titcomb. Equivalence of topologically-algebraic and semitopological functors. Canad. J. Math., 32(l):34–39, 1980. (Zbl. 435.18002, MR 81f:18008)MathSciNetMATHCrossRefGoogle Scholar
  15. [AS81]
    Jiří Adamek and George E. Strecker. Construction of cartesian closed topological hulls. Comment. Math. Univ. Carolinae, 22(2):235–254, 1981. (Zbl. 457.18006, MR 83a:18017)MathSciNetMATHGoogle Scholar
  16. [AS82]
    Jiří Adamek and George E. Strecker. On the largest initial completion of categories of algebras. In Categorical aspects of topology and analysis (Ottawa, Ont., 1980), volume 915 of Lecture Notes in Math., pages 1–15, Berlin — Heidelberg — New York, 1982. Springer-Verlag. (Zbl. 479.18001, MR 83g:18002)CrossRefGoogle Scholar
  17. [MS82]
    A. Melton and George E. Strecker. On the structure of factorization structures. In Category theory (Gummersbach, 1981), volume 962 of Lecture Notes in Math., pages 197–208, Berlin — Heidelberg — New York, 1982. Springer-Verlag. (Zbl. 502.18001, MR 84b:18001)CrossRefGoogle Scholar
  18. [GST83]
    Eraldo Giuli, George E. Strecker, and Anna Tozzi. On e-dense hulls and shape theory. In General topology and its relations to modern analysis and algebra, V (Prague, 1981), volume 3 of Sigma Ser. Pure Math., pages 233–238, Berlin, 1983. Heldermann Verlag. (Zbl. 509.18006, MR 84g:18003)Google Scholar
  19. [ST83]
    George E. Strecker and Tim Titcomb. Faithfulness vs. topologicity. Quaestiones Math., 6:255–264, 1983. (Zbl. 525.18001, MR 84f:18001)MathSciNetCrossRefMATHGoogle Scholar
  20. [Str84]
    George E. Strecker. On cartesian closed topological hulls. In Categorical topology (Toledo, Ohio, 1983), volume 5 of Sigma Ser. Pure Math., pages 523–539, Berlin, 1984. Heldermann Verlag. (Zbl. 548.18006, MR 87f:18006)Google Scholar
  21. [ARS85]
    Jiří Adamek, J. Reiterman, and George E. Strecker. Realization of cartesian closed topological hulls. Manuscripta Math., 53(1–2):1–33, 1985. (Zbl. 573.54006, MR 86m:18005)MathSciNetMATHCrossRefGoogle Scholar
  22. [MSS86]
    A. Melton, D.A. Schmidt, and George E. Strecker. Galois connections and computer science applications. In Category theory and computer programming (Guildford, 1985), volume 240 of Lect. Notes in Comput. Sci, pages 299–312, Berlin — Heidelberg — New York, 1986. Springer-Verlag. (Zbl. 622.06004, MR 88h:68059)CrossRefGoogle Scholar
  23. [HS86]
    Horst Herrlich and George E. Strecker. Cartesian closed topological hulls as injective hulls. Quaestiones Math., 9(1–4):263–280, 1986. (Zbl. 614.18003, MR 88a:18008)MathSciNetMATHCrossRefGoogle Scholar
  24. [MS86]
    A. Melton and George E. Strecker. Structures supporting Galois connections. Technical Report CS-86-1, Kansas State University, 1986.Google Scholar
  25. [BHS86]
    H. Bargenda, Horst Herrlich, and George E. Strecker. Concrete categories and injectivity. In Mathematical foundations of programming semantics (Manhattan, KS, 1985), volume 239 of Lect. Notes in Comput. Sci, pages 42–52, Berlin — Heidelberg — New York, 1986. Springer-Verlag. (Zbl. 597.18008, MR 88a:18009)CrossRefGoogle Scholar
  26. [HSS87]
    Horst Herrlich, G. Salicrup, and George E. Strecker. Factorizations, denseness, separation, and relatively compact objects. Topology Appl., 27(2): 157–169, 1987. (Zbl. 629.18003, MR 89e:18001)MathSciNetMATHCrossRefGoogle Scholar
  27. [MMS87]
    J.M. McDill, A.C. Melton, and George E. Strecker. A category of Galois connections. In Category theory and computer science (Edinburgh, 1987), volume 283 of Lect. Notes in Comput. Sci, pages 290–300, Berlin — Heidelberg — New York, 1987. Springer-Verlag. (Zbl. 649.18003, MR 89e:18009)CrossRefGoogle Scholar
  28. [AS89]
    Jiří Adámek and George E. Strecker. Injectivity of topological categories. Algebra Universalis, 26(3):284–306, 1989. (Zbl. 685.18007, MR 91e:18005)MathSciNetMATHCrossRefGoogle Scholar
  29. [HJS89]
    Andréka H., Greechie R. J., and George E. Strecker. On residuated approximations. In Categorical Methods in Computer Science with Aspects from Topology, volume 393 of Lect. Notes in Comput. Sci, pages 333–339, Berlin — Heidelberg — New York, 1989. Springer-Verlag. (MR 91e:06001)CrossRefGoogle Scholar
  30. [CS90]
    Gabriele Castellini and George E. Strecker. Global closure operators vs. subcategories. Quaestiones Math., 13(3–4):417–424, 1990. (Zbl. 733.18001, MR 92h:18001)MathSciNetMATHCrossRefGoogle Scholar
  31. [HMS91]
    Horst Herrlich, T. Mossakowski, and George E. Strecker. Algebra ∪ topology. In Category theory at work (Bremen, 1990), volume 18 of Res. and Expo, in Math., pages 137–148, Berlin, 1991. Heldermann Verlag. (Zbl. 748.18002, MR 92m:18001)Google Scholar
  32. [CKS92a]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. A factorization of the Pumpluen-Roehrl connection. Topology Appl., 44(1–3):69–76,1992. (Zbl. 774.18002, MR 93f: 18007)MathSciNetCrossRefGoogle Scholar
  33. [CKS92b]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. Categorical closure operators via Galois connections. In W. Gähler et. al., editor, Recent developments of General Topology and its Applications, Mathematical Research, pages 72–79, Berlin, 1992. Akademie-Verlag. (Zbl. 793.18001, MR 94e:06004)Google Scholar
  34. [CKS92c]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. Hereditary and modal closure operators. In R. A. G. Seely, editor, Category Theory 1991, Proceedings of the Summer International Meeting, number 13 in C.M.S. Conference Proceedings, pages 111–132, Providence, RI, 1992. Amer. Math. Soc. (Zbl. 796.18002, MR 93k:18005)Google Scholar
  35. [MSS92]
    A. Melton, Bernd S. W. Schröder, and George E. Strecker. connections. In MFPS 1991, Proceedings of the International Conference 1991, number 598 in Lect. Notes in Comput. Sci, pages 493–506, Berlin — Heidelberg — New York, 1992. Springer-Verlag. (MR 94g:06007)Google Scholar
  36. [CKS93]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. Closure operators and polarities. In Papers on general topology and applications (Madison, WI, 1991), pages 38–52, New York, 1993. New York Acad. Sci. (Zbl. 815.18001, MR 95a:18001)Google Scholar
  37. [EKMS93]
    M. Erné, Jürgen Koslowski, A. Melton, and George E. Strecker. A primer on Galois connections. In Papers on general topology and applications (Madison, WI, 1991) (Ed. Aaron R. Todd), volume 704 of Annals of the New York Academy of Sciences, pages 103–125, New York, 1993. New York Acad. Sci. (Zbl. 809.06006, MR 95g:06011)Google Scholar
  38. [CKS94a]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. Regular closure operators. Appl. Categ. Structures, 2(3):219–244,1994. (Zbl. 801.18003, MR 95h:18001)MathSciNetMATHCrossRefGoogle Scholar
  39. [CKS94b]
    Gabriele Castellini, Jürgen Koslowski, and George E. Strecker. An approach to a dual of regular closure operators. Cahiers Topologie Géom. Différentielle Catégoriques, 35(2):109–128, 1994. (Zbl. 801.18002, MR 95f: 18003)MathSciNetMATHGoogle Scholar
  40. [MSS94]
    Austin Melton, Bernd S.W. Schroeder, and George E. Strecker. Lagois connections — a counterpart to Galois connections. Theoret Comput. Sci., 136(1):79–107, 1994. (Zbl. 873.68053, MR 96f:06006)MathSciNetMATHCrossRefGoogle Scholar
  41. [HS97a]
    Horst Herrlich and George E. Strecker. Categorical topology — its origins, as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971. In Handbook of the history of general topology, Vol. 1, pages 255–341, Dordrecht, 1997. Kluwer Acad. Publ. (Zbl. 906.54001, MR 99f:54003)Google Scholar
  42. [Str00a]
    George E. Strecker. Flows with respect to a functor. Appl. Categ. Structures, 8(3):559–577, 2000.MathSciNetMATHCrossRefGoogle Scholar
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    George E. Strecker. E-M-factorization systems in categories, Encyclopedia of Mathematics, pages 374–375. Kluwer, Amsterdam, 2000.Google Scholar
  44. [Str01]
    George E. Strecker. 10 rules for surviving as a mathematician and teacher This volume.Google Scholar

George E. Strecker’s Monographs

  1. [Str80a]
    George E. Strecker. Introduction to (E,M)-Categories and (E, M)-Functors. Consiglio Nazionale dello Ricerche, Rome, 1980.Google Scholar
  2. [Str80b]
    George E. Strecker. An Introduction to Categorical Methods. Wiskundig Seminarium, Amsterdam, 1980.Google Scholar
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    George E. Strecker. Keeping Dimensions Straight, volume 564 of UMAP Monograph. EDC Inc., Boston, 1981.Google Scholar
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    George E. Strecker. Initial Completions of Concrete Categories. Consiglio Nazionale dello Ricerche, Rome, 1981.Google Scholar
  5. [Str82]
    George E. Strecker. Round Numbers, volume 578 of UMAP Monograph. EDC Inc., Boston, 1982. UMAP Journal III No. 4 (1982),425–454.Google Scholar

George E. Strecker’s Books

  1. [NS71]
    Philip Nanzetta and George E. Strecker. Set theory and topology. Bogden & Quigley, Tarrytown-on-Hudson, N.Y., 1971. (Zbl. 214.00207, MR 57#120)MATHGoogle Scholar
  2. [HS73]
    Horst Herrlich and George E. Strecker. Category theory. An introduction. Allyn and Bacon Inc., Boston, 1973. 2nd edition: Heldermann Verlag, Berlin, 1979. (Zbl. 265.18001/437.18001, MR 57#120/81e:18001)MATHGoogle Scholar
  3. [AHS90]
    Jiři Adámek, Horst Herrlich, and George E. Strecker. Abstract and concrete categories. The joy of cats. John Wiley & Sons Inc., New York, 1990. (Zbl. 695.18001, MR 91h:18001)MATHGoogle Scholar

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Jürgen Koslowski
    • 1
  1. 1.Institut für Theoretische InformatikTechnische Universität BraunschweigBraunschweigGermany

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