Hans-Peter A. Künzi, Salvador Romaguera
Left $K$-completeness of the Hausdorff quasi-uniformity
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 51, 167-176(1997)

MSC:

54E15 Uniform structures and generalizations

54E35 Metric spaces, metrizability

54B20 Hyperspaces

Abstract: Left $K$-completeness of the Hausdorff quasi-uniformity is
investigated.
In particular the restriction of this quasi-uniformity to the
(nonempty) compact subsets of a quasi-metric space is studied.
Among other things it is shown that for any topological space the Hausdorff quasi-uniformity of the
well-monotone quasi-uniformity is left $K$-complete.
Keywords: Left $K$-complete, Smyth complete, Hausdorff quasi-uniformity, Bourbaki quasi-uniformity, well-monotone quasi-uniformity.