Ortho-bases and monotonic properties

Junnila, Heikki J. K.; Künzi, Hans-Peter A.

doi:10.1090/S0002-9939-1993-1165056-6

Ortho-bases and monotonic properties
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by Heikki J. K. Junnila and Hans-Peter A. Künzi PDF

Proc. Amer. Math. Soc. 119 (1993), 1335-1345 Request permission

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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