Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-02-06477-8
Published electronically: May 1, 2002
MathSciNet review: 1920054
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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
  • 4. H.-P.A. Künzi, Nontransitive quasi-uniformities, Publ. Math. Debrecen 55 (1999), 161-167. MR 2000i:54032
  • 5. H.-P. A. Künzi, Remark on a result of Losonczi, Studia Sci. Math. Hung. 36 (2000), 367-370. MR 2001i:54024
  • 6. H.-P.A. Künzi and A. Losonczi, On some cardinal functions related to quasi-uniformities, Houston J. Math. 26 (2000), 299-313. MR 2001k:54008
  • 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
  • 8. H.-P.A. Künzi and S. Watson, A nontransitive space based on combinatorics, Boll. U.M.I. (8) 2-B (1999), 315-317. MR 2000f:54024
  • 9. A. Losonczi, On the cardinality of compatible quasi-uniformities, Topology Appl. 103 (2000), 43-54. MR 2001b:54033
  • 10. A. Losonczi, On the cardinality of $\Pi(\delta)$, Comment. Math. Univ. Carol. (to appear).
  • 11. A.H. Stone, Hereditarily compact spaces, Amer. J. Math. 82 (1960), 900-916. MR 22:11370

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54E15, 54E05, 54A25

Retrieve articles in all journals with MSC (2000): 54E15, 54E05, 54A25


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

DOI: https://doi.org/10.1090/S0002-9939-02-06477-8
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
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

American Mathematical Society