Violator spaces vs closure spaces
نویسندگان
چکیده
Violator Spaces were introduced by J. Matoušek 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 antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces 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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