Symmetrization of Closure Operators and Visibility |
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Authors: | Horst Martini Walter Wenzel |
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Institution: | 1. Fakult?t für Mathematik, Technische Universit?t Chemnitz, D-09107, Chemnitz, Germany
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Abstract: | For an arbitrary set E and a given closure operator
, we want to construct a symmetric closure operator
via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator .
defines a matroid. If
and
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.
Received March 9, 2005 |
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Keywords: | 06A15 05B35 06B05 51D20 52A05 |
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