On the illumination of unbounded closed convex sets
type: Item
instance of: scholarly article
title: On the illumination of unbounded closed convex sets
zbMATH Open document ID: 0771.52002
DOI: 10.1007/BF02808155
author: Károly Bezdek
published in: Israel Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: A closed convex set \(K\subset R^ d\) is called almost bounded if there is a \(d\)-dimensional ball that intersects every supporting hyperplane of \(K\). Let \(L\) denote the orthogonal complementary subspace of the affine hull of the recession cone of \(K\). It is proved here that the minimum number of \(k\)-dimensional subspaces needed to illuminate the \(d\)- dimensional almost bounded convex set \(K\) is not larger than the minimum number of \(k\)-dimensional subspaces of \(L\) needed to illuminate the closure of the projection of \(K\) onto \(L\).
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 219407
zbMATH Keywords: convex body
zbMATH Keywords: illumination
reviewed by: Imre Bárány
MaRDI profile type: Publication
cites work: Q3138750
cites work: The problem of illumination of the boundary of a convex body by affine subspaces
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cites work: Überdeckung eines Eibereiches durch Parallelverschiebung seines offenen Kerns
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full work available at URL: https://doi.org/10.1007/bf02808155
OpenAlex ID: W1979317947
description: scientific article; zbMATH DE number 219407