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Order preserving functions on ordered topological vector spaces

Published online by Cambridge University Press:  17 April 2009

J.C. Candeal ,
E. Induráin  and
G.B. Mehta
J.C. Candeal
Affiliation:
Universidad de ZaragozaDepartamento de Análisis EconómicoFacultad de Ciencias Economicás y Empresariales50005 ZaragozaSpain
E. Induráin
Affiliation:
Universidad Pública de NavarraDepartamento de Matemáticas e InformáticaCampus Arrosadia s.n.E-31006 PamplonaSpain
G.B. Mehta
Affiliation:
University of QueenslandDepartment of EconomicsQueensland 4072Australia
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Abstract

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In this paper we prove the existence of continuous order preserving functions on ordered topological vector spaces in an infinite-dimensional setting. In a certain class of topological vector spaces we prove the existence of topologies for which every continuous total preorder has a continuous order preserving representation and show that the Mackey topology is the finest topology with this property. We also prove similar representation theorems for reflexive Banach spaces and for Banach spaces that may not have a pre-dual.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 55 - 65
Copyright
Copyright © Australian Mathematical Society 1999

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