On a universality property of some abelian Polish groups

• Autorzy: Su Gao , Vladimir Pestov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 22A25: Representations of general topological groups and semigroups
• 47D03: Groups and semigroups of linear operators
• 22A05: Structure of general topological groups
• 54H15: Transformation groups and semigroups
• 43A35: Positive definite functions on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 1
• Strony: 1-15

Daty

wydano

2003

Twórcy

autor

Su Gao

• Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, TX 76203-1430, U.S.A.

autor

Vladimir Pestov

• School 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

Identyfikatory

DOI

10.4064/fm179-1-1