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A note on Ralph Fox's $ \gamma $-space


Author: Hans-Peter A. Künzi
Journal: Proc. Amer. Math. Soc. 91 (1984), 467-470
MSC: Primary 54D18; Secondary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1984-0744650-2
MathSciNet review: 744650
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Abstract: We show that Ralph Fox's construction of a non-quasi-metrizable $ \gamma $-space gives an example of a preorthocompact space that has an open cover that is not quasi-normal.


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

  • [1] R. Engelking, General topology, Monogr. Mat. 60, Polish Scientific Publishers, Warsaw, 1977. MR 0500780 (58:18316b)
  • [2] P. Fletcher and W. F. Lindgren, $ C$-complete quasi-uniform spaces, Arch. Math. 30 (1978), 175-180. MR 0474216 (57:13863)
  • [3] -, Quasi-uniform spaces, Lecture Notes in Pure and Appl. Math., 77, Dekker, New York, 1982. MR 660063 (84h:54026)
  • [4] R. Fox, Pretransitivity and products of suborderable spaces, Topology and Order Structures, Part I, MC Tract 142, Math. Centrum, Amsterdam, 1981. MR 630545 (82j:54010)
  • [5] -, Solution of the $ \gamma $-space problem, Proc. Amer. Math. Soc. 85 (1982), 606-608. MR 660614 (83h:54035)
  • [6] H. J. K. Junnila, Covering properties and quasi-uniformities of topological spaces, Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1978.
  • [7] J. Kofner, Quasi-metrizable spaces, Pacific J. Math. 88 (1980), 81-89.
  • [8] -, On quasi-metrizability, Topology Proc. 5 (1980), 111-138.
  • [9] E. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199-214. MR 0287502 (44:4706)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0744650-2
Keywords: $ \gamma $-space, quasi-normal cover, preorthocompact, weakly orthocompact
Article copyright: © Copyright 1984 American Mathematical Society

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