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An answer to a conjecture on the countable products of $k$-spaces


Author: Huai Peng Chen
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
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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 [Enhancements On Off] (What's this?)

    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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Keywords: <I>k</I>-space, <I>k</I>-system, locally compact, ordinal
Article copyright: © Copyright 1995 American Mathematical Society