Nontransitive quasi-uniformities in the Pervin quasi-proximity class
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- by H.-P. A. Künzi PDF
- Proc. Amer. Math. Soc. 130 (2002), 3725-3730 Request permission
Abstract:
We show that each topological space that does not admit a unique quasi-uniformity possesses a Pervin quasi-proximity class containing at least $2^c$ nontransitive members.References
- 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
- J. Gerlits, H.-P.A. Künzi, A. Losonczi and Z. Szentmiklóssy, The existence of compatible nontransitive totally bounded quasi-uniformities, Topology Appl. 117 (2002), 139–147.
- Hans-Peter A. Künzi, Functorial admissible quasi-uniformities on topological spaces, Topology Appl. 43 (1992), no. 1, 27–36. MR 1141370, DOI 10.1016/0166-8641(92)90151-O
- Hans-Peter A. Künzi, Nontransitive quasi-uniformities, Publ. Math. Debrecen 55 (1999), no. 1-2, 161–167. MR 1708390
- H.-P. A. Künzi, Remark on a result of Losonczi, Studia Sci. Math. Hungar. 36 (2000), no. 3-4, 367–370. MR 1798744, DOI 10.1556/SScMath.36.2000.3-4.10
- Hans-Peter A. Künzi and Attila Losonczi, On some cardinal functions related to quasi-uniformities, Houston J. Math. 26 (2000), no. 2, 299–313. MR 1814240
- H.-P. A. Künzi and M. J. Pérez-Peñalver, The number of compatible totally bounded quasi-uniformities, Acta Math. Hungar. 88 (2000), no. 1-2, 15–23. Third Iberoamerican Conference on Topology and its Applications (Valencia, 1999). MR 1780508, DOI 10.1023/A:1006788124139
- Hans-Peter A. Künzi and Stephen Watson, A nontransitive space based on combinatorics, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 2 (1999), no. 2, 315–317 (English, with Italian summary). MR 1706596
- A. Losonczi, On the cardinality of compatible quasi-uniformities, Topology Appl. 103 (2000), no. 1, 43–54. MR 1746917, DOI 10.1016/S0166-8641(98)00159-X
- A. Losonczi, On the cardinality of $\Pi (\delta )$, Comment. Math. Univ. Carol. (to appear).
- A. H. Stone, Hereditarily compact spaces, Amer. J. Math. 82 (1960), 900–916. MR 120620, DOI 10.2307/2372948
Additional Information
- H.-P. A. Künzi
- Affiliation: Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
- Email: kunzi@maths.uct.ac.za
- Received by editor(s): May 26, 2001
- Received by editor(s) in revised form: July 25, 2001
- Published electronically: May 1, 2002
- Additional Notes: The author acknowledges support by the Swiss National Science Foundation (under grant 20-63402.00) during his stays at the University of Berne, Switzerland.
- Communicated by: Alan Dow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3725-3730
- MSC (2000): Primary 54E15, 54E05, 54A25
- DOI: https://doi.org/10.1090/S0002-9939-02-06477-8
- MathSciNet review: 1920054