  We show that every uniformly recurrent subgroup of a locally compact group is
the family of stabilizers of a minimal action on a compact space. More
generally, every closed invariant subset of the Chabauty space is the family of
stabilizers of an action on a compact space on which the stabilizer map is
continuous everywhere. This answers a question of Glasner and Weiss. We also
introduce the notion of a universal minimal flow relative to a uniformly
recurrent subgroup and prove its existence and uniqueness.
