Full groups of minimal homeomorphisms and Baire category methods
Full groups of minimal homeomorphisms and Baire category methods
We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space $X$ , showing that these groups do not admit a compatible Polish group topology and, in the case of $\mathbb{Z}$ -actions, are coanalytic non-Borel inside $\text{Homeo}(X)$ . We point out that the full group …