Groups not acting on compact metric spaces by homeomorphisms


We show that the direct sum of uncountably many nonAbelian groups does not embed into the group of homeomorphisms of a compact metric space. The main result of this note does not seem to exist in the literature. Among other things, it provides simple examples of left-orderable groups of continuum cardinality which do not embed in Homeo+(R). Theorem 1.1. Let… (More)