Displaying similar documents to “On the iso-taxicab trigonometry.”

Metric spaces with the small ball property

Ehrhard Behrends, Vladimir M. Kadets (2001)

Studia Mathematica

Similarity:

A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...

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...