Displaying similar documents to “Urysohn universal spaces as metric groups of exponent 2”

On natural metrics.

Claudi Alsina, Enric Trillas (1977)

Stochastica

Similarity:

In the present note we study the effective construction of a natural generalized metric structure (on a set), obtaining as particular case the result of Menger. In the case of groups, we analyze its topology and its structure of natural proximity space (in the sense of Efremovic).

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

Enrico Le Donne (2017)

Analysis and Geometry in Metric Spaces

Similarity:

Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory...

Linearly rigid metric spaces and the embedding problem

J. Melleray, F. V. Petrov, A. M. Vershik (2008)

Fundamenta Mathematicae

Similarity:

We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows...