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1 ICJ - Institut Camille Jordan Villeurbanne

Abstract : 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 non-Borel inside the homeomorphism group of $X$. 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 minimal homeomorphism inside the group of all homeomorphisms of $X$.





Author: Tomás Ibarlucia - Julien Melleray -

Source: https://hal.archives-ouvertes.fr/



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