Products of a compact space and a metric space

Tchebycheff Approximation in a Compact Metric Space

The Wijsman structure of a quantale-valued metric space

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

Quantum isometry group of a compact metric space

We give a definition of isometric action of a compact quantum group on a compact metric space, generalizing the definition given by Banica for finite metric spaces, and prove the existence of the universal object in the category of compact quantum groups acting isometrically on a given compact metric space.

On the Conformal Gauge of a Compact Metric Space

In this article we study the Ahlfors regular conformal gauge of a compact metric space (X, d), and its conformal dimension dimAR(X, d). Using a sequence of finite coverings of (X, d), we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gaug...

Dynamical distance as a semi-metric on nuclear conguration space

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.