A general structure for classification

The problem of classifying signals is considered. Typically, a finite number m of pairwise disjoint sets C₁,. . .,C_m of signals is given, and the aim is to synthesize a system that maps the elements of each C_j into a real number a_j so that the numbers a₁,. . .,a_m are distinct. A structure that can perform this classification (for any prescribed distinct a₁,. . .,a_m), assuming only that the C_j are compact subsets of a real normed linear space, is presented