Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 283294 (2009) 

The intersection of convex transversals is a convex polytopeJim Lawrence and Valeriu SoltanDepartment of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA, email: lawrence@gmu.edu, email: vsoltan@gmu.eduAbstract: It is proven that the intersection of convex transversals of finitely many sets in $\R^n$ is a convex polytope, possibly empty. Related results on support hyperplanes and complements of finite unions of convex sets are given. Keywords: convex transversal, polytope, polyhedron, complement Classification (MSC2000): 52A20 Full text of the article:
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