A short proof of Rubin's theorem

2022/03/11 by James Belk, Belk, James, Luke Elliott +3 · 4 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2203.05930

Abstract

In a remarkable theorem, M. Rubin proved that if a group G acts in a locally dense way on a locally compact Hausdorff space X without isolated points, then the space X and the action of G on X are unique up to G-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 X.

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