Topological Dynamics of Closed Subgroups of $S_{\infty }$

Abstract

For $G$ a closed subgroup of $S_{\infty }$, we provide an explicit characterization of the greatest $G$-ambit. Using this, we provide a precise characterization of when $G$ has metrizable universal minimal flow. In particular, each such instance fits into the framework of metrizable flows developed by Kechris-Pestov-Todorcevic and Nguyen Van Thé; as a consequence, each $G$ with metrizable universal minimal flow has the generic point property.

Minor errors and typos have been corrected

References in corpus (1)

• Extremely amenable groups via continuous logic