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

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Categorical Perspectives

Part of the book series: Trends in Mathematics ((TM))

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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.

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References

George E. Strecker’s Topological Articles

  1. 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.

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  2. 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)

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  3. George E. Strecker. On topologies congruent with their classes of dense sets. Technical Report ZW1966–019, Math. Centrum Amsterdam Afd. Zuivere Wisk., 1966.

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  4. 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)

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  5. 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)

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  6. 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)

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  7. Horst Herrlich and George E. Strecker. H -closed spaces and reflective subcategories. Math. Ann., 177:302–309, 1968. (Zbl. 157.29104, MR 38#2744)

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  8. 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)

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  9. 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)

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  10. C. T. Liu and George E. Strecker. Concerning almost realcompactifications. Czechoslovak Math. J., 22:181–190, 1972. (Zbl. 247.54024, MR 46#2644)

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  11. 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)

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  12. 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)

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  13. F. A. Delahan and George E. Strecker. Graphic extensions of mappings. Quaestiones Math., 2:401–417, 1977. (Zbl. 365.54004, MR 58#2692)

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  14. 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).

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George E. Strecker’s Categorical Articles

  1. Horst Herrlich and George E. Strecker. Coreflective subcategories. Trans. Amer. Math. Soc., 157:205–226, 1971. (Zbl. 224.18003, MR 43#6281)

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  2. Horst Herrlich and George E. Strecker. Algebra ∩ topology = compactness. General Topology and Appl., 1:283–287, 1971. (Zbl. 231.18007, MR 46#7349)

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  3. Horst Herrlich and George E. Strecker. Coreflective subcategories in general topology. Fund. Math., 73:199–218, 1972. (Zbl. 231.18008, MR 46#1872)

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  4. 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)

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  5. 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)

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  6. 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)

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  7. 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)

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  8. 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)

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  9. 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)

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  10. 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)

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  11. 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)

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  12. 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)

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  13. 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)

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  14. 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)

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  15. 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)

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  16. 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)

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  17. 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)

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  18. 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)

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  19. George E. Strecker and Tim Titcomb. Faithfulness vs. topologicity. Quaestiones Math., 6:255–264, 1983. (Zbl. 525.18001, MR 84f:18001)

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  20. 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)

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  21. 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)

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  22. 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)

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  23. 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)

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  24. A. Melton and George E. Strecker. Structures supporting Galois connections. Technical Report CS-86-1, Kansas State University, 1986.

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  25. 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)

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  26. 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)

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  27. 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)

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  28. Jiří Adámek and George E. Strecker. Injectivity of topological categories. Algebra Universalis, 26(3):284–306, 1989. (Zbl. 685.18007, MR 91e:18005)

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  29. 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)

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  30. 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)

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  31. 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)

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  32. 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)

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  33. 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)

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  34. 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)

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  35. 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)

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  36. 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)

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  37. 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)

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  38. 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)

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  39. 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)

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  40. 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)

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  41. 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)

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  42. George E. Strecker. Flows with respect to a functor. Appl. Categ. Structures, 8(3):559–577, 2000.

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  43. George E. Strecker. E-M-factorization systems in categories, Encyclopedia of Mathematics, pages 374–375. Kluwer, Amsterdam, 2000.

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  44. George E. Strecker. 10 rules for surviving as a mathematician and teacher This volume.

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George E. Strecker’s Monographs

  1. George E. Strecker. Introduction to (E,M)-Categories and (E, M)-Functors. Consiglio Nazionale dello Ricerche, Rome, 1980.

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  2. George E. Strecker. An Introduction to Categorical Methods. Wiskundig Seminarium, Amsterdam, 1980.

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  3. George E. Strecker. Keeping Dimensions Straight, volume 564 of UMAP Monograph. EDC Inc., Boston, 1981.

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  4. George E. Strecker. Initial Completions of Concrete Categories. Consiglio Nazionale dello Ricerche, Rome, 1981.

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  5. George E. Strecker. Round Numbers, volume 578 of UMAP Monograph. EDC Inc., Boston, 1982. UMAP Journal III No. 4 (1982),425–454.

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George E. Strecker’s Books

  1. Philip Nanzetta and George E. Strecker. Set theory and topology. Bogden & Quigley, Tarrytown-on-Hudson, N.Y., 1971. (Zbl. 214.00207, MR 57#120)

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  2. 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)

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  3. 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)

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Other References

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  4. P. Antoine. Extension minimale de la catégorie des espaces topologiques. C. R. Acad. Sci., Paris, Ser. A, 262:1389–1392, 1966.

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  17. Horst Herrlich. Cartesian closed topological categories. Math. Colloq. Univ. Cape Town, 9:1–16, 1974.

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  21. Horst Herrlich and M. Hušek. Categorical Topology. In M. Hušek and J. van Mill, editors, Recent Progress in General Topology, pages 369–403, Amsterdam, 1992. Elsevier.

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  22. Horst Herrlich and M. Hušek. Some open categorical problems in top. Appl. Categ. Structures, 1:1–14, 1993.

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  23. Horst Herrlich and W. Meyer. Factorization of flows and completenes of categories. Quaestiones Math., 17:1–11, 1994.

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  1. Institut für Theoretische Informatik, Technische Universität Braunschweig, Braunschweig, Germany

    Jürgen Koslowski

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  1. Jürgen Koslowski
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  1. Institut für Theoretische Informatik, TU Braunschweig, 38023, Braunschweig, Germany

    Jürgen Koslowski

  2. Department of Mathematics and Computer Science, Kent State University, Kent, OH, 44242, USA

    Austin Melton

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Koslowski, J. (2001). Contributions and Importance of Professor George E. Strecker’s Research. In: Koslowski, J., Melton, A. (eds) Categorical Perspectives. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1370-3_5

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  • DOI: https://doi.org/10.1007/978-1-4612-1370-3_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7117-8

  • Online ISBN: 978-1-4612-1370-3

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