Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T08:14:45.975Z Has data issue: false hasContentIssue false

Strongly zero-dimensional bispaces

Published online by Cambridge University Press:  09 April 2009

Hans-Peter A. Künzi
Affiliation:
University of BerneSidlerstrasse 53012 Berne, Switzerland
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.

Let Cb be the admissible functorial quasi-uniformity on the completely regular bispaces which is spanned by the upper quasi-uniformity on the real line. Answering a question posed by B. Banaschewski and G. C. L. Brümmer in the affirmative we show that CbX is transitive for every strongly zero-dimensional bispace X.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Banaschewski, B. and Brümmer, G. C. L., ‘Strongly zero-dimensionality of biframes and bispaces’, Quaestiones Math. 13 (1990), 273290.CrossRefGoogle Scholar
[2]Brümmer, G. C. L., ‘On certain factorizations of functors into the category of quasi- uniform spaces’, Quaestiones Math. 2 (1977), 5984.CrossRefGoogle Scholar
[3]Brümmer, G. C. L., ‘On the non-unique extension of topological to bitopological properties’, Categorical Aspects of Topology and Analysis (Proc. Conf., Ottawa, 1980), Lecture Notes in Math. (Springer) 915 (1982), 5067.Google Scholar
[4]Engelking, R., General Topology, Heldermann, Berlin, 1989.Google Scholar
[5]Fletcher, P. and Lindgren, W. F., ‘Quasi-uniformities with a transitive base’, Pacific J. Math. 43 (1972), 619631.CrossRefGoogle Scholar
[6]Fletcher, P. and Lindgren, W. F., Quasi-uniform Spaces, Lecture Notes Pure Appi. Math. 77, Marcel Dekker, New York, 1982.Google Scholar
[7]Fora, A. A., ‘Strongly zero-dimensional bitopological spaces’, J. Univ. Kuwait (Sci.) 11 (1984), 181190.Google Scholar
[8]Künzi, H. P. A., ‘Topological spaces with a unique compatible quasi-proximity’, Arch. Math. 43 (1984), 559561.CrossRefGoogle Scholar
[9]Künzi, H. P. A., ‘Topological spaces with a unique compatible quasi-uniformity’, Canad. Math. Bull. 29 (1986), 4043.CrossRefGoogle Scholar
[10]Künzi, H. P. A., ‘Some remarks on quasi-uniform spaces’, Glasgow Math. J. 31 (1989), 309320.Google Scholar
[11]Künzi, H. P. A., ‘Functorial admissible quasi-uniformities on topological spaces’, Top. Appl. 43 (1992), 2736.CrossRefGoogle Scholar
[12]Lene, E. P., ‘Bitopological spaces and quasi-uniform spaces’, Proc. London Math. Soc. 17 (1967), 241256.CrossRefGoogle Scholar
[13]Reilly, I. L., ‘Zero dimensional bitopological spaces’, Nederl. Akad. Wetensch., Proc. Ser. A 76 = Indag. Math. 35 (1973), 127131.CrossRefGoogle Scholar
[14]Salbany, S., ‘Quasi-uniformities and quasi-pseudometrics’, Math. Colloq. Univ. Cape Town 6 (19701971), 88102.Google Scholar