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Determining the continuous affine structure of a topological convex space

Published online by Cambridge University Press:  03 December 2007

A. Pulgarín
A. Pulgarín
Affiliation:
Departamento de Matemáticas, Escuela Politécnica de la Universidad de Extremadura, Avenida Universidad s/n, 10071 Cáceres, Spain (aapulgar@unex.es)
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Abstract

We characterize a topological convex space $C$ in terms of the family $\mathcal{A}(C)$ of real continuous affine functions on $C$. Our main result states that two topological convex spaces $C_1$ and $C_2$ are affine-homeomorphic if and only if $\mathcal{A}(C_1)$ and $\mathcal{A}(C_2)$ are isomorphic as ordered unital vector spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 6 , December 2007 , pp. 1329 - 1334
Copyright
2007 Royal Society of Edinburgh

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