Tychonoff reflection in products and the -topology on function spaces
Author:
Stephen Watson
Journal:
Proc. Amer. Math. Soc. 108 (1990), 557-559
MSC:
Primary 54C35; Secondary 54B10, 54D45
DOI:
https://doi.org/10.1090/S0002-9939-1990-1007518-5
MathSciNet review:
1007518
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Abstract | References | Similar Articles | Additional Information
Abstract: We show that if is a topological space such that
, the topology on
generated by the cozero sets, is not locally compact, then there is a regular space
such that
. We use the
-topology on the space of continuous functions
(where
is an open cover of
) which was defined by Arens and Dugundji in 1950.
- [1] Richard Arens and James Dugundji, Topologies for function spaces, Pacific J. Math. 1 (1951), 5–31. MR 43447
- [2] Shinpei Oka, Tychonoff functor and product spaces, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 4, 97–100. MR 482671
- [3] Petr Simon, Completely regular modification and products, Comment. Math. Univ. Carolin. 25 (1984), no. 1, 121–128. MR 749120
- [4] A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), no. 1, 544–561 (German). MR 1512595, https://doi.org/10.1007/BF01782364
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-1007518-5
Article copyright:
© Copyright 1990
American Mathematical Society