Classifiers on relatively compact sets

The problem of classifying signals is of interest in several application areas. Typically we are given a finite number m of pairwise disjoint sets C/sub 1/, ..., C/sub m/ of signals, and we would like to synthesize a system that maps the elements of each C/sub j/ into a real number a/sub j/, such that the numbers a/sub 1/, ..., a/sub m/ are distinct. In a recent paper it is shown that this classification can be performed by certain simple structures involving linear functionals and memoryless nonlinear elements, assuming that the C/sub j/ are compact subsets of a real normed linear space. Here we give a similar solution to the problem under the considerably weaker assumption that the C/sub j/ are relatively compact and are of positive distance from each other. An example is given in which the C/sub j/ are subsets of L/sub p/(a,b), 1/spl les/p>