Topological dynamics beyond Polish groups
Gianluca Basso
Université de Lausanne, Switzerland; Université Claude Bernard yon 1, Université de Lyon, Villeurbanne, FranceAndy Zucker
University of California – San Diego, La Jolla, USA
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