Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T18:05:08.446Z Has data issue: false hasContentIssue false
  • English
  • Français

A nontrivial T1-space admitting a unique quasi-proximity

Published online by Cambridge University Press:  18 May 2009

Hans-Peter A. Künzi  and
Stephen Watson
Hans-Peter A. Künzi
Affiliation:
Department of Mathematics, University of Berne, Sldlerstrasse 5, CH-3012 Berne, Switzerland E-mail: [email protected]
Stephen Watson
Affiliation:
Department of Mathematics, York University, North York, Ontario, CanadaM3J 1P3 E-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct a T1-space that is not hereditarily compact, although each of its open sets is the intersection of two compact open sets. The search for such a space was motivated by a problem in the theory of quasi-proximities.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 207 - 213
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Brümmer, G. C. L. and Künzi, H. P. A., Sobrification and bicompletion of totally bounded quasi–uniform spaces, Math. Proc. Camb. Phil. Soc. 101 (1987), 237–247.Google Scholar
2.Ferrer, J., On topological spaces with a unique quasi-proximity, Quaestiones Math. 17 (1994), 479–486.CrossRefGoogle Scholar
3.Fletcher, P. and Lindgren, W. F., Quasi-uniform spaces (Dekker, 1982).Google Scholar
4.Künzi, H. P. A., Topological spaces with a unique compatible quasi-proximity, Arch. Math. 43 (1984), 559–561.CrossRefGoogle Scholar
5.Künzi, H. P. A., Some remarks on quasi-uniform spaces, Glasgow Math. J. 31 (1989), 309–320.CrossRefGoogle Scholar
6.Künzi, H. P. A., Quasi-uniform spaces—eleven years later, Topology Proc. 18 (1993), 143–171.Google Scholar
7.Lindgren, W. F., Topological spaces with a unique compatible quasi-uniformity, Canad. Math. Bull. 14 (1971), 369–372.CrossRefGoogle Scholar
8.Lindgren, W. F., Topological spaces with unique quasi–uniform structure, Arch. Math. 22 (1971), 417–419.CrossRefGoogle Scholar
9.Stone, A. H., Hereditarily compact spaces, Amer. J. Math. 82 (1960), 900–916.CrossRefGoogle Scholar