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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the set of extreme points of a convex body


Author: James B. Collier
Journal: Proc. Amer. Math. Soc. 47 (1975), 184-186
DOI: https://doi.org/10.1090/S0002-9939-1975-0350625-2
MathSciNet review: 0350625
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Abstract: We prove the following: Given a subset $ X$ of a compact 0-dimensional metric space $ Z$ and an integer $ d \geqslant 3$, there is a homeomorphism of $ Z$ into the boundary of a convex body $ C$ in $ {E^d}$ mapping $ X$ onto the set of extreme points of $ C$ if and only if $ X$ is a $ {G_\delta }$ set with at least $ d + 1$ points.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0350625-2
Article copyright: © Copyright 1975 American Mathematical Society