  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.
