** 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.*