On a universality property of some abelian Polish groups

Details On a universality property of some abelian Polish groups On a universality property of some abelian Polish groups

2002-05-28

arxiv.org/abs/math/0205291v1

Fundamenta Mathematicae 179 (2003), 1-15.

Mathematics

General Topology

16 pages, LaTeX 2e

Scientific paper

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.

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