A Polish metric space whose group of isometries induces a universal relation for Polish group actions
Volume 239 / 2017
Fundamenta Mathematicae 239 (2017), 43-49
MSC: Primary 03E15; Secondary 54H05.
DOI: 10.4064/fm341-1-2017
Published online: 28 April 2017
Abstract
We show that there exists a Polish metric space $(X,d)$ such that the action of its isometry group on $X$ produces an equivalence relation which is universal for relations induced by a Borel action of a Polish group on a standard Borel space.
