a1 Mathematics Department, The University, Leicester LEI 7RH.
§1. Introduction and Summary. Throughout X is a complete separable metric space. We write K1 for the family of non-empty compact subsets of X. K1 may be endowed with a metric (first introduced by Hausdorff) under which K1 is complete and separable. We shall make use of the subbase for this metrizable topology of K1 given by sets of the two forms
for U open in X (see Kuratowski  or E. Michael  for a discussion of topologies on the space of subsets of X). if we shall be concerned with sets in [0, 1] × X which are universal for . To define these let us make the convention that, for D [0, 1] × X, we write
D is said to be universal for if
(Received January 02 1974)