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Totally bounded frame quasi-uniformities

Peter Fletcher; Worthen N. Hunsaker; William F. Lindgren — 1993

Commentationes Mathematicae Universitatis Carolinae

This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity $◃$ on a frame $L$ there is a totally bounded quasi-uniformity on $L$ that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines $◃$ . The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum $ψ L$ and the compactification $ℜ L$ of a uniform frame $(L, 𝐔)$ are meaningful for quasi-uniform frames. If $𝐔$ is a totally bounded quasi-uniformity...

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