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Extreme point axioms for closure spaces
Authors:Kazutoshi Ando
Institution:Department of Systems Engineering, Shizuoka University, Hamamatsu, 432-8561 Shizuoka, Japan
Abstract:A pair (X,τ) of a finite set X and a closure operator τ:2X→2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X,τ), the extreme point operator ex:2X→2X is defined as ex(A)={p|pA,pτ(A-{p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectively.
Keywords:Closure operator  Matroid  Antimatroid  Convex geometry  Choice function  Extreme point
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