Rigid sets in the Hilbert cube

AbstractLet X be a compact metric space with no isolated points. Then we may embed X as a subset of the Hilbert cube Q (X⊂Q) so that the only homeomorphism of X onto itself that extends to a homeomorphism of Q is the identity homeomorphism. Such an embedding is said to be rigid. In fact, there are uncountably many rigid embeddings Xα of X in Q so that for α≠β and any homeomorphism h of Q, h(Xα)∩Xβ is a Z-set in Q and a nowhere dense subset of each of h(Xα) and Xβ