Affinely embeddable convex sets
type: Item
instance of: scholarly article
title: Affinely embeddable convex sets
zbMATH Open document ID: 0625.52002
DOI: 10.1007/BF01950997
author: T. Bisztriczky
author: Jonathan Schaer
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The authors prove the following Helly-type theorem: Let \({\mathcal A}_ r=\{A_ 1\),..., \(A_ r\}\) be a collection of \(r\geq 4\) mutually disjoint closed convex sets in the real projective plane \(P^ 2\) with the property that no element of \({\mathcal A}_ r\) is contained in a convex hull of any other two elements of \({\mathcal A}_ r\). Then \({\mathcal A}_ r\) is affinely embeddable, i.e. there is a line in \(P^ 2\) which does not meet any of the \(A_ i\).
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 4015575
zbMATH Keywords: Helly-type theorem
zbMATH Keywords: convex sets
zbMATH Keywords: affinely embeddable
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Theorems on two separated convex bodies
cites work: Q3247592
cites work: Q3243607
cites work: Order and Topology in Projective Planes
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description: scientific article; zbMATH DE number 4015575