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

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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Additional Information

DOI:
http://dx.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