We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.
Mathematics Subject Classification. 28B15 06A06 91B16.
Keywords. Topological vector space; preordered real cone; sublinear order-preserving function; decreasing scale.
Comments. This article is in final form.