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 acts in a locally dense way on a locally compact Hausdorff space without isolated points, then the space and the action of on are unique up to -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 .
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