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Proceedings of the American Mathematical Society

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On Archimedean ordered vector spaces and a characterization of simplices


Authors: Gerhard Gierz and Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 116 (1992), 369-375
MSC: Primary 46A55; Secondary 46A40
DOI: https://doi.org/10.1090/S0002-9939-1992-1095222-9
MathSciNet review: 1095222
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Abstract: We show that a convex subset $ K$ of a linear space is a simplex if and only if it is line compact and every nonempty intersection of two translates of $ K$ is a homothet of $ K$. This answers a problem posed by Rosenthal. The proof uses a reformulation of this problem in terms of Archimedean ordered spaces


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1095222-9
Keywords: Simplices, Archimedean ordered spaces, sublattices of $ C(K)$
Article copyright: © Copyright 1992 American Mathematical Society