Sublinear and continuous order-preserving functions for noncomplete   preorders
  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. 
Gianni Bosi and Magali E. Zuanon