SEPARATING POINTS OF BETA-N BY MINIMAL FLOWS

We consider minimal left ideals L of the universal semigroup compactif ication betaS of a topological semigroup S. We show that the envelopin g semigroup of L is homeomorphically isomorphic to betaS if and only i f given q not-equal r in betaS, there is some p in the smallest ideal of betaS with qp not-equal rp. We derive several conditions, some invo lving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = N, an d the compactification is betaN. Included is the statement that some s et A whose characteristic function is uniformly recurrent has q is-an- element-of cl(A) and r is-not-an-element-of cl(A).