On the existence of utility functions ii

This paper is a continuation of the author's earlier paper on the existence of utility functions. In the earlier paper the idea of a separable system on a preordered topological space (X,≾,t) was introduced to prove a fundamental theorem on the existence of a continuous utility function on (X,≾,t). This theorem allowed us, for example, to obtain Peleg's utility representation theorem as an immediate corollary. In fact, it even allowed us to...