A note on Ralph Fox’s $\gamma$-space
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- by Hans-Peter A. Künzi PDF
- Proc. Amer. Math. Soc. 91 (1984), 467-470 Request permission
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
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- P. Fletcher and W. F. Lindgren, $C$-complete quasi-uniform spaces, Arch. Math. (Basel) 30 (1978), no. 2, 175–180. MR 474216, DOI 10.1007/BF01226037
- Peter Fletcher and William F. Lindgren, Quasi-uniform spaces, Lecture Notes in Pure and Applied Mathematics, vol. 77, Marcel Dekker, Inc., New York, 1982. MR 660063
- Ralph Fox, Pretransitivity and products of suborderable spaces, Topology and order structures, Part 1 (Lubbock, Tex., 1980) Math. Centre Tracts, vol. 142, Math. Centrum, Amsterdam, 1981, pp. 115–118. MR 630545
- Ralph Fox, Solution of the $\gamma$-space problem, Proc. Amer. Math. Soc. 85 (1982), no. 4, 606–608. MR 660614, DOI 10.1090/S0002-9939-1982-0660614-X H. J. K. Junnila, Covering properties and quasi-uniformities of topological spaces, Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1978. J. Kofner, Quasi-metrizable spaces, Pacific J. Math. 88 (1980), 81-89. —, On quasi-metrizability, Topology Proc. 5 (1980), 111-138.
- Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502
Additional Information
- © Copyright 1984 American Mathematical Society
- 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