违反者空间与闭包空间
Violator spaces vs closure spaces
摘要：
Violator Spaces由J. Matousek等人在2008年引入，作为线性规划问题的推广。凸几何是Edelman和Jamison在1985年发明的，作为凸性的适当组合抽象。凸几何由反交换闭包算子定义。研究了Violator空间与闭包空间之间的相互关系，证明了Violator映射可以由一个弱形式的闭包算子定义。此外，我们证明了具有唯一基的Violator空间满足反交换和Krein-Milman性质。
英文摘要：
Violator Spaces were introduced by J. Matousek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by anti-exchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator mapping may be defined by a week version of closure operators. Moreover, we prove that violator spaces with an unique basis satisfies the anti-exchange and the Krein-Milman properties.
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