Among the many semigroups which can be derived from a given compact (jointly continuous) semigroup S is the semigroup 2s consisting of its non-empty compact subsets; the product is the usual one defined by the rule EF = {xy:xεE, yεF}. The Vietoris or finite topology on 2s (in which a base for the open sets is obtained by taking all sets of the form for l ≦i ≦n} as Vl, V2,…, Vn run over all finite collections of open subsets of S) makes 2s a compact, jointly continuous semigroup. The topology has a long history, having been introduced by Vietoris in 1923 and studied by Michael[4]. The utility of the topological semigroup was established by Hofmann and Mostert [3; see especially Section 3.7]; in fact they prefer to produce directly the uniform structure on 2s rather than the topology.