Topology Atlas Document # ppae-01


Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space

Gianni Bosi and Magalí E. Zuanon

Proceedings of the Ninth Prague Topological Symposium (2001) pp. 1-8

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.

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Copyright © 2002 Charles University and Topology Atlas. Published April 2002.