A topological space without a complete quasi-uniformity
Authors:
Hans-Peter A. Künzi and Peter Fletcher
Journal:
Proc. Amer. Math. Soc. 90 (1984), 611-615
MSC:
Primary 54E15; Secondary 54D20
DOI:
https://doi.org/10.1090/S0002-9939-1984-0733415-3
MathSciNet review:
733415
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Abstract | References | Similar Articles | Additional Information
Abstract: We show that an example of Burke and van Douwen has no complete quasi-uniformity. Moreover, we show that it is almost finitely-fully normal but not almost ${\aleph _0}$-fully normal.
- Giovanni Aquaro, Intorno ad una generalizzazione degli spazi paracompatti, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 38 (1965), 824–827 (Italian). MR 195044 D. K. Burke and E. K. van Douwen, On countably compact extensions of normal locally compact $M$-spaces, Set-Theoretic Topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975-1976), Academic Press, New York, 1977, pp. 81-90.
- 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
- Klaas Pieter Hart, More on M. E. Rudin’s Dowker space, Proc. Amer. Math. Soc. 86 (1982), no. 3, 508–510. MR 671226, DOI https://doi.org/10.1090/S0002-9939-1982-0671226-6 H. J. K. Junnila, Covering properties and quasi-uniformities of topological spaces, Ph. D. Thesis, Virginia Polytechnic Inst. and State Univ., Blacksburg, Va., 1978.
- M. J. Mansfield, Some generalizations of full normality, Trans. Amer. Math. Soc. 86 (1957), 489–505. MR 93753, DOI https://doi.org/10.1090/S0002-9947-1957-0093753-5
- K. Morita, Paracompactness and product spaces, Fund. Math. 50 (1961/62), 223–236. MR 132525, DOI https://doi.org/10.4064/fm-50-3-223-236
- William J. Pervin, Uniformization of neighborhood axioms, Math. Ann. 147 (1962), 313–315. MR 140082, DOI https://doi.org/10.1007/BF01440952
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Additional Information
Keywords:
Almost <!– MATH ${\aleph _0}$ –> <IMG WIDTH="27" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\aleph _0}$">-fully normal,
almost finitely-fully normal,
complete quasi-uniformity
Article copyright:
© Copyright 1984
American Mathematical Society