On the facial structure of a convex body
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- by J. B. Collier PDF
- Proc. Amer. Math. Soc. 61 (1976), 367-370 Request permission
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 $d = 3$.References
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- Victor Klee and Michael Martin, Semicontinuity of the face-function of a convex set, Comment. Math. Helv. 46 (1971), 1–12. MR 282190, DOI 10.1007/BF02566824
Additional Information
- © Copyright 1976 American Mathematical Society
- 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