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H. Martini; W. Wenzel : A characterization of convex sets via visibility

H. Martini; W. Wenzel : A characterization of convex sets via visibility

Author(s) :
H. Martini; W. Wenzel
Title :
A characterization of convex sets via visibility
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-10, 2000
Mathematics Subject Classification :
51D05 [ Abstract geometries ]
52A01 [ Axiomatic and generalized geometric convexity ]
52A20 [ Convex sets in n dimensions ]
Abstract :
For a subset K \subseteq {\Bb R}^n and E : = {\Bb R}^n \K we consider some operator \sigma : {\cal P}(E) \rightarrow {\cal P}(E) induced by visibility in a canonical way. If K is compact and E is connected, we prove that K is convex if and only if \sigma is a closure operator.
Keywords :
convexity, closure operators, visibility, compact and convex body
Language :
english
Publication time :
8/2000