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Tychonoff's Theorem in a category
Author(s):
Maria
Manuel
Clementino;
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:
A categorical proof of Tychonoff's Theorem on the productivity of compact topological spaces is provided.
References:
- 1.
- N. Bourbaki, Topologie générale, ch. I et II, third edition (Paris 1961). MR 25:4480
- 2.
- E. \v{C}ech, Topologické prostory (Prague 1959); English transl., Wiley, New York, 1966. MR 21:2962; MR 35:2254.
- 3.
- D. Dikranjan and E. Giuli, Closure Operators I, Topology Appl. 27 (1987) 129-143. MR 89e:18002
- 4.
- D. Dikranjan and E. Giuli, Compactness, minimality and closedness with respect to a closure operator, in: Categorical Topology and its relations to Analysis, Algebra and Combinatorics (World Scientific, Singapore 1989) pp. 284-296. MR 91e:18008
- 5.
- D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators (Kluwer Academic Publishers 1995).
- 6.
- R. Engelking, General Topology, revised and completed edition (Heldermann Verlag, Berlin 1989). MR 91c:54001
- 7.
- P. J. Freyd and G. M. Kelly, Categories of continuous functors, I, J. Pure Appl. Algebra 2 (1972) 169-191. Erratum ibid. 4 (1974) 121. MR 48:369; MR 49:2877
- 8.
- Z. Frolík, On the topological product of paracompact spaces, Bull. Acad. Pol. Sci. Sér. Math. 8 (1960) 747-750. MR 23:A2859
- 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 22:8479
- 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) 79-107. MR 95d:54009
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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
DOI:
10.1090/S0002-9939-96-03435-1
PII:
S 0002-9939(96)03435-1
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 of article:
Copyright
1996,
American Mathematical Society
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