On the non-existence of certain group topologies

Volume 187 / 2005

Christian Rosendal Fundamenta Mathematicae 187 (2005), 213-228 MSC: Primary 03E15. DOI: 10.4064/fm187-3-2


Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of $\mathbb R$ cannot be a Polish group either.


  • Christian RosendalMathematics 253-37
    California Institute of Technology
    Pasadena, CA 91125, U.S.A.
    Department of Mathematics
    University of Illinois at Urbana-Champaign
    1409 W. Green Street (MC-382)
    Urbana, IL 61801-2975, U.S.A.

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