English

Full groups of minimal homeomorphisms

Logic 2014-02-04 v2 Dynamical Systems

Abstract

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space XX, showing that these groups do not admit a compatible Polish group topology and, in the case of Z\Z-actions, are coanalytic non-Borel inside \Homeo(X)\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 minimal homeomorphism inside \Homeo(X)\Homeo(X).

Keywords

Cite

@article{arxiv.1309.3114,
  title  = {Full groups of minimal homeomorphisms},
  author = {Tomás Ibarlucia and Julien Melleray},
  journal= {arXiv preprint arXiv:1309.3114},
  year   = {2014}
}
R2 v1 2026-06-22T01:25:35.139Z