Full Groups of Minimal Homeomorphisms
نویسنده
چکیده
We study full groups ofminimal 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 Z-actions, are coanalytic non-Borel inside Homeo(X). We then focus on the closure of the full group of a uniquely ergodic homeomorphism, elucidating underwhich conditions this group has a comeager (or, equivalently in that case, dense) conjugacy class, and point out that when that happens the closure of the full group is simple and satisfies the automatic continuity property. We also prove that the full group of a uniquely ergodic homeomorphism is topologically simple.
منابع مشابه
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 Z-actions, are coanalytic nonBorel inside Homeo(X). We point out that the full group of a minimal homeomorphism is topologically simple. We also study some properties of the closure of the full group of a...
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