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Martini, Horst; Wenzel, Walter : Symmetrization of Closure Operators and Visibility

Martini, Horst ; Wenzel, Walter : Symmetrization of Closure Operators and Visibility

Author(s):
Martini, Horst
Wenzel, Walter
Title:
Symmetrization of Closure Operators and Visibility
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 1, 2001
Mathematics Subject Classification:
06A15 [ Galois correspondences, closure operators ]
05B35 [ Matroids, geometric lattices ]
06B05 [ Structure theory ]
51D20 [ Combinatorial geometries ]
52A05 [ Convex sets without dimension restrictions ]
Abstract:
For an arbitrary set E and a closure operator defined on the power set of E we construct a symmetric closure operator in a rather canonical way. If E is finite the corresponding symmetric closure operator defines a matroid. Moreover, the symmetrization process is applied to closure operators induced by visibility.
Keywords:
Closure operators, symmetric and algebraic closure operators, lattices, matroids, visibility problems, convexity
Language:
English
Publication time:
9 / 2001