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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
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?)

  • [1] A. V. Arhangelskii, Factor mapping of metric spaces, Soviet Math. Dokl. 5 (1964), 368-371.
  • [2] A. V. Arhangel′skiĭ, Bicompact sets and the topology of spaces., Trudy Moskov. Mat. Obšč. 13 (1965), 3–55 (Russian). MR 0195046
  • [3] Yoshio Tanaka, Some necessary conditions for products of 𝑘-spaces, Bull. Tokyo Gakugei Univ. (4) 30 (1978), 1–16. MR 512222
  • [4] Yoshio Tanaka, Point-countable 𝑘-systems and products of 𝑘-spaces, Pacific J. Math. 101 (1982), no. 1, 199–208. MR 671852
  • [5] 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: k-space, k-system, locally compact, ordinal
Article copyright: © Copyright 1995 American Mathematical Society

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