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Nontransitive quasi-uniformities in the Pervin quasi-proximity class

Author: H.-P. A. Künzi
Journal: Proc. Amer. Math. Soc. 130 (2002), 3725-3730
MSC (2000): Primary 54E15, 54E05, 54A25
Published electronically: May 1, 2002
MathSciNet review: 1920054
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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.

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Additional Information

H.-P. A. Künzi
Affiliation: Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa

Keywords: Nontransitive quasi-uniformity, quasi-proximity class, hereditarily compact, Pervin quasi-uniformity, irreducible, hereditarily precompact
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
Article copyright: © Copyright 2002 American Mathematical Society

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