The Topological Foundation of Information Theory

Classical information theory has been conducted exclusively in spaces with a countablebasis, Type I. We establish a theory of information in a space with an uncountable basis,Type II. Type I is one coordinate of Type II and in the unified space, Type I ⊂ Type II.All previous work in Type I remains valid. The expansion of the space to include Type IIopens new domains where Type I methods cannot be formulated.