Non-abelian group structure on the Urysohn universal space

Michal Doucha. "Non-abelian group structure on the Urysohn universal space." Fundamenta Mathematicae 228.3 (2015): 251-263. <http://eudml.org/doc/282582>.

@article{MichalDoucha2015,
abstract = {We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.},
author = {Michal Doucha},
journal = {Fundamenta Mathematicae},
keywords = {Urysohn universal metric space; Graev metric; free group},
language = {eng},
number = {3},
pages = {251-263},
title = {Non-abelian group structure on the Urysohn universal space},
url = {http://eudml.org/doc/282582},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Michal Doucha
TI - Non-abelian group structure on the Urysohn universal space
JO - Fundamenta Mathematicae
PY - 2015
VL - 228
IS - 3
SP - 251
EP - 263
AB - We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.
LA - eng
KW - Urysohn universal metric space; Graev metric; free group
UR - http://eudml.org/doc/282582
ER -