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