Nontransitive quasi-uniformities in the Pervin quasi-proximity class
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- by H.-P. A. Künzi
- Proc. Amer. Math. Soc. 130 (2002), 3725-3730
- DOI: https://doi.org/10.1090/S0002-9939-02-06477-8
- Published electronically: May 1, 2002
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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
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Bibliographic 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