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