Linearly rigid metric spaces and the embedding problem

J. Melleray, F. V. Petrov, and A. M. Vershik. "Linearly rigid metric spaces and the embedding problem." Fundamenta Mathematicae 199.2 (2008): 177-194. <http://eudml.org/doc/282810>.

@article{J2008,
abstract = {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 us to give a simple proof of the linear rigidity of the Urysohn space and some other metric spaces. Various properties of linearly rigid spaces and related spaces are considered.},
author = {J. Melleray, F. V. Petrov, A. M. Vershik},
journal = {Fundamenta Mathematicae},
keywords = {linearly rigid metric spaces; Kantorovich-Rubinstein norm; Urysohn space; isometric embedding},
language = {eng},
number = {2},
pages = {177-194},
title = {Linearly rigid metric spaces and the embedding problem},
url = {http://eudml.org/doc/282810},
volume = {199},
year = {2008},
}

TY - JOUR
AU - J. Melleray
AU - F. V. Petrov
AU - A. M. Vershik
TI - Linearly rigid metric spaces and the embedding problem
JO - Fundamenta Mathematicae
PY - 2008
VL - 199
IS - 2
SP - 177
EP - 194
AB - 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 us to give a simple proof of the linear rigidity of the Urysohn space and some other metric spaces. Various properties of linearly rigid spaces and related spaces are considered.
LA - eng
KW - linearly rigid metric spaces; Kantorovich-Rubinstein norm; Urysohn space; isometric embedding
UR - http://eudml.org/doc/282810
ER -