Tychonoff’s Theorem in a category
HTML articles powered by AMS MathViewer
- by Maria Manuel Clementino and Walter Tholen PDF
- Proc. Amer. Math. Soc. 124 (1996), 3311-3314 Request permission
Abstract:
A categorical proof of Tychonoff’s Theorem on the productivity of compact topological spaces is provided.References
- N. Bourbaki, Éléments de mathématique. Première partie. (Fascicule II.) Livre III: Topologie générale. Chapitre 1: Structures topologiques. Chapitre. 2: Structures uniformes, Hermann, Paris, 1961 (French). Troisiéme édition entiérement refondue; Actualités Sci. Indust., No. 1142. MR 0141067
- Eduard Čech, Topologické prostory, Nakladatelství Československé Akademie Věd, Prague, 1959 (Czech). With supplements: J. Novák, Construction of certain important topological spaces; M. Katětov, Fully normal spaces. MR 0104205
- 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, DOI 10.1016/0166-8641(87)90100-3
- 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
- D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators (Kluwer Academic Publishers 1995).
- 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
- P. J. Freyd and G. M. Kelly, Categories of continuous functors. I, J. Pure Appl. Algebra 2 (1972), 169–191. MR 322004, DOI 10.1016/0022-4049(72)90001-1
- 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 125559
- K. Kuratowski, Evaluation de la classe borélienne d’un ensemble de points à l’aide des symboles logiques, Fund. Math. 17 (1931) 249-272.
- S. Mrówka, Compactness and product spaces, Colloq. Math. 7 (1959), 19–22. MR 117704, DOI 10.4064/cm-7-1-19-22
- A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935) 767-776.
- J. J. C. Vermeulen, Proper maps of locales, J. Pure Appl. Algebra 92 (1994), no. 1, 79–107. MR 1259670, DOI 10.1016/0022-4049(94)90047-7
Additional Information
- Maria Manuel Clementino
- Affiliation: Departamento de Matemática, Apartado 3008, 3000 Coimbra, Portugal
- Email: clementino@gemini.ci.uc.pt
- Walter Tholen
- Affiliation: Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3
- Email: tholen@mathstat.yorku.ca
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3311-3314
- MSC (1991): Primary 18B30, 54B30, 54D30, 54A05
- DOI: https://doi.org/10.1090/S0002-9939-96-03435-1
- MathSciNet review: 1340379