Topological dynamics beyond Polish groups

  • Gianluca Basso

    Université de Lausanne, Switzerland; Université Claude Bernard yon 1, Université de Lyon, Villeurbanne, France
  • Andy Zucker

    University of California – San Diego, La Jolla, USA
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Abstract

When is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of . We introduce a class of groups, the CAP groups, which provides a neat generalization of this to all topological groups. We prove a number of characterizations of this class, having very different flavors, and use these to prove that the class of CAP groups enjoys a number of nice closure properties. As a concrete application, we compute the universal minimal flow of the homeomorphism groups of several scattered topological spaces, building on recent work of Gheysens.

Cite this article

Gianluca Basso, Andy Zucker, Topological dynamics beyond Polish groups. Comment. Math. Helv. 96 (2021), no. 3, pp. 589–630

DOI 10.4171/CMH/521