Mathematical logic seminar: Sumun Iyer (Carnegie Mellon University)

Homeomorphism groups of connected spaces Abstract: Let X be a compact metric space. The group of homeomorphisms of X with the uniform convergence topology is a Polish topological group. Projective Fraisse categories provide a way to approximate compact metric spaces and their groups of homeomorphisms via categories of finite graphs. We introduce a new combinatorial property of a projective Fraisse category called the approximate Ramsey property that corresponds to extreme amenability of the approximated homeomorphism group. We prove that the group of homeomorphisms of the universal pseudo-solenoid has non-metrizable universal minimal flow.