Abstract: | Let be an interval order on a topological space (X, τ), and let x ˜* y if and only if y z x z], and x ˜** y if and only if z x z y]. Then ˜* and ˜** are complete preorders. In the particular case when is a semiorder, let x ˜0 y if and only if x ˜* y and x ˜** y. Then ˜0 is a complete preorder, too. We present sufficient conditions for the existence of continuous utility functions representing ˜*, ˜** and ˜0, by using the notion of strong separability of a preference relation, which was introduced by Chateauneuf (Journal of Mathematical Economics, 1987, 16, 139–146). Finally, we discuss the existence of a pair of continuous functions u, υ representing a strongly separable interval order on a measurable topological space (X, τ, μ,
). |