Martini, Horst ; Wenzel, Walter : A Unified Approach to Illumination and Visibility Problems via Closure Operators

Author(s):

Martini, Horst
Wenzel, Walter

Title:

A Unified Approach to Illumination and Visibility Problems via Closure Operators

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 1, 2004

Mathematics Subject Classification:

52A20			[ Convex sets in $n$ dimensions ]
52A37			[ Other problems of combinatorial convexity ]
03G05			[ Boolean algebras ]
06A15			[ Galois correspondences, closure operators ]
06B23			[ Complete lattices, completions ]

Abstract:

We present a unified approach to the notions of illumination and visibility of convex bodies in terms of closure operators. Moreover, we study also the complete lattice of a more general framework of closure operators.

Keywords:

convex bodies, illumination, visibility, closure operators, complete lattices, Boolean lattices, Hadwiger's covering problem

Language:

English

Publication time:

2 / 2004