Adaricheva, Kira2016-02-092016-02-092011Adaricheva Kira; 2011; Representing finite convex geometries by relatively convex sets; arXiv.orghttp://nur.nu.edu.kz/handle/123456789/1205A closure system with the anti-exchange axiom is called a convex geometry. One geometry is called a sub-geometry of the other if its closed sets form a sublattice in the lattice of closed sets of the other. We prove that convex geometries of relatively convex sets in n-dimensional vector space and their nite sub-geometries satisfy the n-Carousel Rule, which is the strengthening of the n-Carath eodory property. We also nd another property, that is similar to the simplex partition property and does not follow from 2-Carusel Rule, which holds in sub-geometries of 2-dimensional geometries of relatively convex sets.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICSfinite convex geometriesArticle