On a universality property of some abelian Polish groups
Volume 179 / 2003
Fundamenta Mathematicae 179 (2003), 1-15 MSC: Primary 22A05, 54H05; Secondary 22A25, 43A35, 47D03, 54H15. DOI: 10.4064/fm179-1-1
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.