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A note on uniform ordered spaces

Part of: Lattices Special properties

Published online by Cambridge University Press:  09 April 2009

Hans-Peter A. Künzi
Hans-Peter A. Künzi
Affiliation:
Department of MathematicsUniversity of BernSidlerstr. 5, 3012 Bern, Switzerland
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Abstract

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We characterize the generalized ordered topological spaces X for which the uniformity (X) is convex. Moreover, we show that a uniform ordered space for which every compatible convex uniformity is totally bounded, need not be pseudocompact.

MSC classification

Secondary: 06B30: Topological lattices, order topologies 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 349 - 352
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Corson, H. H. and Isbell, J. R., ‘Euclidean covers of topological spaces’, Quart. J. Math. Oxford Ser. (2) 11 (1960), 34–42.CrossRefGoogle Scholar
[2]Fletcher, P. and Lindgren, W. F., Quasi-uniform spaces (Lecture Notes in Math., Dekker, New York, 1982).Google Scholar
[3]Fletcher, P., Junnila, H. and Lindgren, W., ‘Another note on bounded paracompactness’, manuscript.Google Scholar
[4]Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, Princeton, N. J., 1960).CrossRefGoogle Scholar