On a universality property of some abelian Polish groups

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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.
16 pages, LaTeX 2e

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General Topology, Logic, Primary 22A05, 54H05; Secondary 22A25, 43A35, 47D03, 54H15

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http://salesiana.dossiersoluciones.com/handle/123456789/137125

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205291
 http://arxiv.org/abs/math/0205291
 Fundamenta Mathematicae 179 (2003), 1-15.

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arXiv