On Archimedean ordered vector spaces and a characterization of simplices
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- by Gerhard Gierz and Boris Shekhtman PDF
- Proc. Amer. Math. Soc. 116 (1992), 369-375 Request permission
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 spacesReferences
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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