Related papers: Plastic metric spaces and groups

Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball-bodies, endowed with the Hausdorff metric. "Ball bodies" are convex bodies which are…

In this paper we define a notion of S-extension for a metric space and study minimality and coherence of S-extensions. We show that every S-extension can be identified with an algebraic object. We use this algebraic representation to give a…

This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed…

We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…

A round metric space is the one in which closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which interior of each closed ball is the corresponding open ball. In this, article we…

We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning separable spaces appeared in various papers in the last…

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…

It is proved that a straight projective-metric space has an open set of centers, if and only if it is either the hyperbolic or a Minkowskian geometry. It is also shown that if a straight projective-metric space has some finitely many…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary…

The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…

In this paper we prove that generic metric spaces are everywhere dense in the proper class of all metric spaces endowed with the Gromov-Hausdorff distance.

We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also show that the Lipschitz-free space over a proper ultrametric space is isometric to…

We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing…

We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected first countable space is the image of a nonseparably connected complete metric space…

We constract various subgroups of the group of isometries of universal Urysohn spaces (unique complete separable metric space which is iniversal and homogeneous) including abelian groups which act transitively, and free groups which are…

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…