Illumination and visibility problems in terms of closure operators
type: Item
instance of: scholarly article
title: Illumination and visibility problems in terms of closure operators
zbMATH Open document ID: 1074.52001
author: Horst Martini
author: Walter Wenzel
published in: Beiträge zur Algebra und Geometrie
publication date: 2004-09-10T00:00:00Z
full work available at URL: https://eudml.org/doc/125234
full work available at URL: 21.html
review text: This paper continues the subject considered earlier by these authors in [Aequationes Math. 64, 128--135 (2002; Zbl 1013.52005)]. Recall that a point \(x\) of the boundary \(\partial (K)\) of a convex body \(K \subset R^n\) is called to be illuminated by a point \(z \not \in K\) if there exists a point \(y \in \text{ int} (K)\) such that \(x \in yz\). Moreover, we say that a set \(S\) disjoint with \(K\) illuminates \(\partial (K)\) if every point of \(\partial (K)\) is illuminated by a point of \(S\). The authors present a few conditions equivalent to the second definition. They are expressed in terms of closure operators.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 2100247
zbMATH Keywords: convex body
zbMATH Keywords: illumination
zbMATH Keywords: visibility
zbMATH Keywords: Hadwiger's covering problem
zbMATH Keywords: closure operator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2100247