A note on weak separability

Here subsets of the real line are given the subspace topology, and Cartesian products of topological spaces are given the product topology. Monotone means weakly increasing or weakly decreasing with respect to the natural ordering of R. This article comments on joint continuity that enables one to remove a certain amount of confusion about a small point in the celebrated paper "The Structure of Utility Functions." The question at issue is whether it is necessary for Gorman's results that the domains of his utility functions be not merely connected, but in fact path-connected, topological spaces.