Geodesic
On a universality property of some abelian Polish groups
Su Gao 1   ; Vladimir Pestov 2
1 Department of Mathematics P.O. Box 311430 University of North Texas Denton, TX 76203-1430, U.S.A.
2 School of Mathematical and Computing Sciences Victoria University of Wellington P.O. Box 600 Wellington, New Zealand and Department of Mathematics and Statistics University of Ottawa Ottawa, ON, K1N 6N5, Canada
Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 1-15 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm179-1-1
Keywords: every abelian polish group topological factor group closed subgroup full unitary group separable hilbert space strong operator topology follows orbit equivalence relations induced abelian polish group actions borel reducible orbit equivalence relations induced actions unitary group

Su Gao  1   ; Vladimir Pestov  2

1 Department of Mathematics P.O. Box 311430 University of North Texas Denton, TX 76203-1430, U.S.A.
2 School of Mathematical and Computing Sciences Victoria University of Wellington P.O. Box 600 Wellington, New Zealand and Department of Mathematics and Statistics University of Ottawa Ottawa, ON, K1N 6N5, Canada 
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Su Gao; Vladimir Pestov. On a universality property of some abelian Polish groups. Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 1-15. doi: 10.4064/fm179-1-1

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