Replacing convex sets by polytopes

S. Gallivan1; J. Zaks

doi:10.1090/S0002-9939-1975-0380627-1

Replacing convex sets by polytopes

S. Gallivan1, J. Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A conjecture of A. J. Hoffman is settled by showing that if P is a ri-polytope in E, if compact convex subsets C.are such that every (-dimensional affine flat that meets P also meets U _.Cthen there exist polytopes such that every i-flat that meets P also meets U.D., provided Counterexamples are given for the cases where.

Original language	English
Pages (from-to)	351-357
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	50
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1975-0380627-1
State	Published - Jul 1975

Keywords

Affine flat
Compact convex s
D-polytope

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1975-0380627-1

Cite this

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title = "Replacing convex sets by polytopes",

abstract = "A conjecture of A. J. Hoffman is settled by showing that if P is a ri-polytope in E, if compact convex subsets C.are such that every (-dimensional affine flat that meets P also meets U \_.Cthen there exist polytopes such that every i-flat that meets P also meets U.D., provided Counterexamples are given for the cases where.",

keywords = "Affine flat, Compact convex s, D-polytope",

author = "S. Gallivan1 and J. Zaks",

year = "1975",

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AU - Gallivan1, S.

AU - Zaks, J.

PY - 1975/7

Y1 - 1975/7

N2 - A conjecture of A. J. Hoffman is settled by showing that if P is a ri-polytope in E, if compact convex subsets C.are such that every (-dimensional affine flat that meets P also meets U _.Cthen there exist polytopes such that every i-flat that meets P also meets U.D., provided Counterexamples are given for the cases where.

AB - A conjecture of A. J. Hoffman is settled by showing that if P is a ri-polytope in E, if compact convex subsets C.are such that every (-dimensional affine flat that meets P also meets U _.Cthen there exist polytopes such that every i-flat that meets P also meets U.D., provided Counterexamples are given for the cases where.

KW - Affine flat

KW - Compact convex s

KW - D-polytope

UR - https://www.scopus.com/pages/publications/84966237321

U2 - 10.1090/S0002-9939-1975-0380627-1

DO - 10.1090/S0002-9939-1975-0380627-1

M3 - Article

AN - SCOPUS:84966237321

SN - 0002-9939

VL - 50

SP - 351

EP - 357

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

Replacing convex sets by polytopes

Abstract

Keywords

ASJC Scopus subject areas

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