On Archimedean ordered vector spaces and a characterization of simplices

Author:

Gierz Gerhard,Shekhtman Boris

Abstract

We show that a convex subset K 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 K is a homothet of K K . This answers a problem posed by Rosenthal. The proof uses a reformulation of this problem in terms of Archimedean ordered spaces

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 57;Alfsen, Erik M.,1971

2. Graduate Texts in Mathematics, Vol. 3;Schaefer, Helmut H.,1971

3. Die Grundlehren der mathematischen Wissenschaften, Band 215;Schaefer, Helmut H.,1974

4. Simplexes and vector lattices;Kendall, David G.;J. London Math. Soc.,1962

5. W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam and Berlin, 1971.

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