Department of Mathematics, UCI

Introduction. Statistical metric spaces, introduced by K. Menger in [5], are a generalization of metric spaces in which distances are given by distribution functions rather than by numbers (1). Just as with metric spaces, there is no a priori topology. But whereas metric spaces have a single natural topology, there are many structures, satisfying some or all of the axioms of a to1>ology, that may be associated with a statistical metric space in a natural way. One such structure for statistical metric spaces was introduced by B. Schweizer and .A. Sklar in [7] (2).