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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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Paracompactness of Pixley-Roy hyperspaces. I
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by Hidenori Tanaka PDF
Proc. Amer. Math. Soc. 85 (1982), 108-112 Request permission

Abstract:

In this paper, we will study the relations between the paracompactness of a Pixley-Roy hyperspace $\mathcal {F}\left [ X \right ]$ and the paracompactness of the subspace ${\mathcal {F}_2}\left [ X \right ]$. We will give the affirmative answer to H. Bennett’s problem.
References
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  • H. R. Bennett, W. G. Fleissner, and D. J. Lutzer, Ultraparacompactness in certain Pixley-Roy hyperspaces, Fund. Math. 111 (1981), no. 1, 11–18. MR 607915, DOI 10.4064/fm-111-1-11-18
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  • Carl Pixley and Prabir Roy, Uncompletable Moore spaces, Proceedings of the Auburn Topology Conference (Auburn Univ., Auburn, Ala., 1969; dedicated to F. Burton Jones on the occasion of his 60th birthday), Auburn Univ., Auburn, Ala., 1969, pp. 75–85. MR 0397671
    • T. Przymusiński, Paracompactness of Pixley-Roy hyperspaces, Notices Amer. Math. Soc. 25 (1978), A-501. —, Normality and paracompactness of Pixley-Roy hypersurfaces, Fund. Math. (to appear).
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 108-112
  • MSC: Primary 54B20; Secondary 54D18, 54F05
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0647909-0
  • MathSciNet review: 647909