2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63748We 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.8 pagesGeneral Topology28B15, 06A06, 91B16text