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Proceedings of the American Mathematical Society

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

 

 

On the facial structure of a convex body


Author: J. B. Collier
Journal: Proc. Amer. Math. Soc. 61 (1976), 367-370
MSC: Primary 52A20
DOI: https://doi.org/10.1090/S0002-9939-1976-0425770-4
MathSciNet review: 0425770
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Abstract: The family formed by taking the relative interior of each face of a $ d$-dimensional convex body $ C$ is a partition of $ C$. It is shown here that the subfamily consisting of all the $ (d - 2)$-dimensional sets has a quotient topology which is paracompact and this is used to prove a property of the set of extreme points when $ d = 3$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0425770-4
Article copyright: © Copyright 1976 American Mathematical Society