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Tychonoff's Theorem in a category

Authors: Maria Manuel Clementino and Walter Tholen
Journal: Proc. Amer. Math. Soc. 124 (1996), 3311-3314
MSC (1991): Primary 18B30, 54B30, 54D30, 54A05
MathSciNet review: 1340379
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Abstract | References | Similar Articles | Additional Information

Abstract: A categorical proof of Tychonoff's Theorem on the productivity of compact topological spaces is provided.

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  • 1. N. Bourbaki, Éléments de mathématique. Première partie. (Fascicule II.) Livre III: Topologie générale. Chapitre 1: Structures topologiques. Chapitre. 2: Structures uniformes, Troisiéme édition entiérement refondue, Actualités Sci. Indust., No. 1142. Hermann, Paris, 1961 (French). MR 0141067
  • 2. Eduard Čech, Topologické prostory, With supplements: J. Novák, Construction of certain important topological spaces; M. Katětov, Fully normal spaces, Nakladatelství Československé Akademie Věd, Prague, 1959 (Czech). MR 0104205
    Eduard Čech, Topological spaces, Revised edition by Zdeněk Frolík and Miroslav Katětov. Scientific editor, Vlastimil Pták. Editor of the English translation, Charles O. Junge, Publishing House of the Czechoslovak Academy of Sciences, Prague; Interscience Publishers John Wiley & Sons, London-New York-Sydney, 1966. MR 0211373
  • 3. Dikran Dikranjan and Eraldo Giuli, Closure operators. I, Proceedings of the 8th international conference on categorical topology (L’Aquila, 1986), 1987, pp. 129–143. MR 911687,
  • 4. Dikran Dikranjan and Eraldo Giuli, Compactness, minimality and closedness with respect to a closure operator, Categorical topology and its relation to analysis, algebra and combinatorics (Prague, 1988) World Sci. Publ., Teaneck, NJ, 1989, pp. 284–296. MR 1047908
  • 5. D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators (Kluwer Academic Publishers 1995).
  • 6. Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
  • 7. P. J. Freyd and G. M. Kelly, Categories of continuous functors. I, J. Pure Appl. Algebra 2 (1972), 169–191. MR 0322004,
    P. J. Freyd and G. M. Kelly, Erratum: “Categories of continuous functors. I “ (J. Pure Appl. Algebra 2 (1972), 169-191), J. Pure Appl. Algebra 4 (1974), 121. MR 0338111,
  • 8. Z. Frolík, On the topoligical product of paracompact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 747–750 (English, with Russian summary). MR 0125559
  • 9. K. Kuratowski, Evaluation de la classe borélienne d'un ensemble de points à l'aide des symboles logiques, Fund. Math. 17 (1931) 249-272.
  • 10. S. Mrówka, Compactness and product spaces, Colloq. Math. 7 (1959), 19–22. MR 0117704
  • 11. A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935) 767-776.
  • 12. J. J. C. Vermeulen, Proper maps of locales, J. Pure Appl. Algebra 92 (1994), no. 1, 79–107. MR 1259670,

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Additional Information

Maria Manuel Clementino
Affiliation: Departamento de Matemática, Apartado 3008, 3000 Coimbra, Portugal

Walter Tholen
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3

Received by editor(s): November 30, 1994
Received by editor(s) in revised form: May 3, 1995
Additional Notes: Partial financial assistance by Centro de Matemática da Universidade de Coimbra, by the Natural Sciences and Engineering Research Council of Canada and by a NATO Collaborative Research Grant (no. 940847) is gratefully acknowledged. Work on this paper was completed while both authors were guests of the University of L’Aquila (Italy)
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society