The Euclidean distance construction of order homomorphisms
The Euclidean distance technique of Arrow and Hahn is used to construct an upper semicontinuous order homomorphism (partial utility function) from (X,\(\succ)\) to \(({\mathbb{R}},>)\), where X is a closed, convex subset of \({\mathbb{R}}^ N\) and \(\succ\) is a continuous strict partial order on X. It is also shown that the order homomorphism is upper semicontinuous as a function on \(X\times {\mathcal P}(X)\), where \({\mathcal P}(X)\) is the set of continuous strict partial orders on X, taken with the topology of closed convergence.
scientific article; zbMATH DE number 4045438