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Proceedings of the American Mathematical Society

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

 

 

Ortho-bases and monotonic properties


Authors: Heikki J. K. Junnila and Hans-Peter A. Künzi
Journal: Proc. Amer. Math. Soc. 119 (1993), 1335-1345
MSC: Primary 54E15; Secondary 54D20, 54E35
DOI: https://doi.org/10.1090/S0002-9939-1993-1165056-6
MathSciNet review: 1165056
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Abstract: We study monotonic properties in the sense of Gartside and Moody. Among other things we show that each space with an ortho-base admits a monotonic quasi-uniformity and that the fine quasi-uniformity of a topological space which admits a monotonic quasi-uniformity need not be monotonic. Furthermore we give an example of a countable space that does not admit any monotonic quasi-uniformity. As a byproduct of our investigations we obtain a new characterization of the topological spaces having an ortho-base.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1165056-6
Keywords: Ortho-base, proto-metrizable, monotonically orthocompact, monotonically normal, monotonic quasi-uniformity
Article copyright: © Copyright 1993 American Mathematical Society