On a universality property of some abelian Polish groups

Volume 179 / 2003

Su Gao, Vladimir Pestov 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.


  • Su GaoDepartment of Mathematics
    P.O. Box 311430
    University of North Texas
    Denton, TX 76203-1430, U.S.A.
  • Vladimir PestovSchool of Mathematical
    and Computing Sciences
    Victoria University of Wellington
    P.O. Box 600
    Wellington, New Zealand
    Department of Mathematics and Statistics
    University of Ottawa
    Ottawa, ON, K1N 6N5, Canada

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