Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Paracompactness of Pixley-Roy hyperspaces. II

Author: Hidenori Tanaka
Journal: Proc. Amer. Math. Soc. 85 (1982), 113-118
MSC: Primary 54B20; Secondary 54D18, 54F05
MathSciNet review: 647909
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we will study the paracompactness of Pixley-Roy hyperspaces of products. We will prove that if $ \mathcal{F}\left[ X \right]$ is paracompact (resp. hereditarily paracompact), then $ \mathcal{F}\left[ {{X^2}} \right]$ is paracompact (resp. hereditarily paracompact). This is the positive answer to T. Przymusiński's problem.

References [Enhancements On Off] (What's this?)

  • [1] H. Bennet, W. Fleissner and D. Lutzer, Ultraparacompactness in certain Pixley-Roy hyperspaces, Fund. Math. 111 (1980), 11-18. MR 607915 (82k:54010)
  • [2] E. K. van Douwen, The Pixley-Roy topology on spaces of subsets, Set Theoretic Topology (G. M. Reed, editor), Academic Press, New York, 1977, pp. 111-134. MR 0440489 (55:13364)
  • [3] R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977. MR 0500780 (58:18316b)
  • [4] D. Lutzer, Pixley-Roy topology, Topology Proc. 3 (1978), 139-158. MR 540485 (80m:54012)
  • [5] C. Pixley and P. Roy, Uncompletable Moore spaces, Proc. Auburn Topology. Conf. (Auburn, Ala., 1969), Auburn Univ., Auburn, Ala., 1969, pp. 78-85. MR 0397671 (53:1529)
  • [6] T. Przymusiński, Normality and paracompactness of Pixley-Roy hyperspaces, Fund. Math. (to appear). MR 641305 (83b:54007)
  • [7] M. E. Rudin, Pixley-Roy and the Souslin line, Proc. Amer. Math. Soc. 74 (1979), 128-134. MR 521886 (80c:54030)
  • [8] H. Tanaka, Paracompactness of Pixley-Roy hyperspaces. I, Proc. Amer. Math. Soc. 85 (1982), 108-112. MR 647909 (83h:54007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B20, 54D18, 54F05

Retrieve articles in all journals with MSC: 54B20, 54D18, 54F05

Additional Information

Keywords: Paracompact, hereditarily paracompact, Pixley-Roy hyperspace, Moore space
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society