Splitting metrics by T0-quasi-metrics

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Data mining for cones of metrics , quasi - metrics , m - hemi - metrics and ( m , s ) - super - metrics

Partial quasi-metrics

In this article we introduce and investigate the concept of a partial quasi-metric and some of its applications. We show that many important constructions studied in Matthews’s theory of partial metrics can still be used successfully in this more general setting. In particular we consider the bicompletion of the quasi-metric space that is associated with a partial quasi-metric space and study i...

On approximating planar metrics by tree metrics

We combine the results of Bartal [Proc. 37th FOCS, 1996, pp. 184–193] on probabilistic approximation of metric spaces by tree metrics, with those of Klein, Plotkin and Rao [Proc. 25th STOC, 1993, pp. 682–690] on decompositions of graphs without small Ks,s minors (such as planar graphs) to show that metrics induced by such graphs (with unit lengths on the edges) can be probabilistically approxim...

Fuzzy quasi-metrics for the Sorgenfrey line

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...