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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An answer to a conjecture on the countable products of $k$-spaces
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by Huai Peng Chen PDF
Proc. Amer. Math. Soc. 123 (1995), 583-587 Request permission

Abstract:

In this paper the author shows: Theorem (CH). There is a ${k_\omega }$-space X which is not locally compact but for which ${X^\omega }$ has a k-system. This answers a conjecture of Y. Tanaka
References
    A. V. Arhangelskii, Factor mapping of metric spaces, Soviet Math. Dokl. 5 (1964), 368-371.
  • A. V. Arhangel′skiĭ, Bicompact sets and the topology of spaces., Trudy Moskov. Mat. Obšč. 13 (1965), 3–55 (Russian). MR 0195046
  • Yoshio Tanaka, Some necessary conditions for products of $k$-spaces, Bull. Tokyo Gakugei Univ. (4) 30 (1978), 1–16. MR 512222
  • Yoshio Tanaka, Point-countable $k$-systems and products of $k$-spaces, Pacific J. Math. 101 (1982), no. 1, 199–208. MR 671852
  • Yoshio Tanaka, On the products of $k$-spaces question, Questions Answers Gen. Topology 1 (1983), no. 1, 36–50. MR 698037
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 583-587
  • MSC: Primary 54D50; Secondary 54B10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1273481-X
  • MathSciNet review: 1273481