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

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
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