Martini, Horst; Wenzel, Walter Illumination and visibility problems in terms of closure operators. (English) Zbl 1074.52001 Beitr. Algebra Geom. 45, No. 2, 607-614 (2004). 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. Reviewer: Marek Lassak (Bydgoszcz) Cited in 8 Documents MSC: 52A01 Axiomatic and generalized convexity 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) Keywords:convex body; illumination; visibility; Hadwiger’s covering problem; closure operator Citations:Zbl 1013.52005 PDFBibTeX XMLCite \textit{H. Martini} and \textit{W. Wenzel}, Beitr. Algebra Geom. 45, No. 2, 607--614 (2004; Zbl 1074.52001) Full Text: EuDML EMIS