On basis of the meanwhile classical continuous multi-utility representation theorem of Levin on locally compact and $\sigma$-compact Hausdorff-spaces the question of characterizing all topological spaces $(X,t)$ for which every closed and semi-closed preorder respectively admits a continuous...

We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that...

Let (X,t) be a topological space. Then a preorder ≾ on (X,t) has a continuous multi-utility representation if there exists a family F of continuous and isotonic real-valued functions f on (X,≾,t) such that for all x∈X and all y∈X the inequalities x≾y mean that for all f∈F the...