An embedding version of Rubin's theorem

Abstract: Rubin's theorem asserts that if $Γ\curvearrowright X$ and $Δ\curvearrowright Y$ are Rubin actions, then any group isomorphism $Γ\cong Δ$ induces an equivariant homeomorphism $Y\cong X$. We provide an embedding version of Rubin's theorem highlighting group embeddings that induce a spatial equivariant map of a certain form. We further showcase instances of such embeddings between generalized Brin-Thompson groups.