Descriptive set-theoretic aspects of closed sets of uniqueness in the non-abelian setting
Volume 265 / 2022
Studia Mathematica 265 (2022), 77-109 MSC: Primary 43A46; Secondary 03E15. DOI: 10.4064/sm210603-25-10 Published online: 22 April 2022
We study the family of closed sets of (extended) uniqueness of a locally compact group $G$ which is not necessarily abelian. We prove some preservation properties concerning this family of sets as well as their operator-theoretic counterpart, locate their descriptive complexity and establish sufficient conditions for the non-existence of a Borel basis.