Non-abelian group structure on the Urysohn universal space
Volume 228 / 2015
Fundamenta Mathematicae 228 (2015), 251-263
MSC: Primary 22A05; Secondary 54E50, 03C98.
DOI: 10.4064/fm228-3-3
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.
