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A note on the groups of finite type and the Hartman–Mycielski construction

Volume 164 / 2021

Vladimir G. Pestov Colloquium Mathematicum 164 (2021), 171-174 MSC: Primary 22A10; Secondary 46L10. DOI: 10.4064/cm8285-6-2020 Published online: 31 August 2020


Ando, Matsuzawa, Thom, and Törnquist have resolved a problem by Sorin Popa by constructing an example of a Polish group of unitary operators with the strong operator topology, whose left and right uniform structures coincide, but which does not embed into the unitary group of a finite von Neumann algebra. The question remained whether such a group can be connected. Here we observe that a connected (in fact, homeomorphic to the Hilbert space) example is obtained from the example of the above authors via the Hartman–Mycielski construction.


  • Vladimir G. PestovInstituto de Matemática e Estatística
    Universidade Federal da Bahia
    Ondina, Salvador, BA, 40.170-115, Brasil
    Department of Mathematics and Statistics
    University of Ottawa
    Ottawa, ON, K1N 6N5, Canada

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