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Symmetrization of Closure Operators and Visibility
Horst Martini and Walter Wenzel
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
{fmartini, walterg}@mathematik.tu-chemnitz.de
Annals of Combinatorics 9 (4) p.431-450 December, 2005
AMS Subject Classification: 06A15, 05B35, 06B05, 51D20, 52A05
Abstract:
For an arbitrary set E and a given closure operator σ:P(E)→P(E), we want to construct a symmetric closure operator : P(E)→P(E) via some ― possibly infinite ― iteration process. If E is finite, the corresponding symmetric closure operator defines a matroid. If E = and s is the convex closure operator, turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by visibility.

Keywords: closure operator, symmetric and finitary closure operator, lattice, matroid, visibility problem, illumination problem, convexity

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