A Classification of Factors, II

Abstract

The algebraic invariant r_∞(M) of a factor M, introduced in an earlier paper and called the asymptotic ratio set, is shown to be closed for any factor M. As a consequence, this set must be one of the following sets: (i) the empty set, (ii) {0}, (iii) {1}, (iv) a one parameter family of sets {0, xⁿ; n=0, ±1, …}, 0<x<1. (v) all non-negative reals, (iv) {0.1}.