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Strongly zero-dimensional bispaces

Part of: Special categories Special properties Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

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

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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.

Keywords

strongly zero-dimensionalsemi-continuous quasi-uniformityfunctorial quasi-uniformitycompletely regular bispacetransitive quasi-uniformitynon-archimedeanly quasi-pseudo-metrizable.

MSC classification

Secondary: 54E15: Uniform structures and generalizations 54E55: Bitopologies 18B30: Categories of topological spaces and continuous mappings 54F45: Dimension theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 327 - 337
Copyright
Copyright © Australian Mathematical Society 1992

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