  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 $X$.
