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Sublinear and continuous order-preserving functions for noncomplete preorders

Gianni Bosi·Magali E. Zuanon
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Abstract

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.

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Gianni Bosi, Magali E. Zuanon. 2002-04-09. Sublinear and continuous order-preserving functions for noncomplete preorders. https://arxiv.org/abs/math/0204101

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