Proceedings of the American Mathematical Society

Author(s): H.-P. A. Künzi
Journal: Proc. Amer. Math. Soc. 130 (2002), 3725-3730.
MSC (2000): Primary 54E15, 54E05, 54A25
Posted: 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

nontransitive members.

1.: P. Fletcher and W.F. Lindgren, Quasi-Uniform Spaces, Lecture Notes Pure Appl. Math. 77, Dekker, New York, 1982. MR 84h:54026
2.: 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.
3.: H.-P.A. Künzi, Functorial admissible quasi-uniformities on topological spaces, Topology Appl. 43 (1992), 27-36. MR 93g:54041
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7.: H.-P.A. Künzi and M.J. Pérez-Peñalver, The number of compatible totally bounded quasi-uniformities, Acta Math. Hung. 88 (2000), 15-23. MR 2001h:54045
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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54E15, 54E05, 54A25

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

DOI: 10.1090/S0002-9939-02-06477-8
PII: S 0002-9939(02)06477-8
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
Posted: 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 of article: Copyright 2002, American Mathematical Society

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