English

A short proof of Rubin's theorem

Group Theory 2023-02-23 v3 Dynamical Systems

Abstract

In a remarkable theorem, M. Rubin proved that if a group GG acts in a locally dense way on a locally compact Hausdorff space XX without isolated points, then the space XX and the action of GG on XX are unique up to GG-equivariant homeomorphism. Here we give a short, self-contained proof of Rubin's theorem, using equivalence classes of ultrafilters on a poset to reconstruct the points of the space XX.

Keywords

Cite

@article{arxiv.2203.05930,
  title  = {A short proof of Rubin's theorem},
  author = {James Belk and Luke Elliott and Francesco Matucci},
  journal= {arXiv preprint arXiv:2203.05930},
  year   = {2023}
}

Comments

10 pages, includes an appendix on algebraic disjointness omitted from the published version

R2 v1 2026-06-24T10:09:56.715Z