  A homeomorphism on a compact metric space is said hyper-expansive if every
pair of different compact sets are separated by the homeomorphism in the
Hausdorff metric. We characterize such dynamics as those with a finite number
of orbits and whose non-wandering set is the union of the repelling and the
attracting periodic orbits. We also give a characterization of compact metric
spaces admiting hyper-expansive homeomorphisms.
