Topological Dynamics of Closed Subgroups of S_∞

2014/04/20 by Zucker, Andy
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1404.5057

Abstract

For G a closed subgroup of S_∞, 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.

Related

• Some universal constructions in abstract topological dynamics
• Universal flows of closed subgroups of S_∞ and relative extreme amenability
• A direct solution to the Generic Point Problem
• Universal minimal flow in the language of near filters and its applications
• Projectivity in topological dynamics