Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 283-294 (2009)

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The intersection of convex transversals is a convex polytope

Jim Lawrence and Valeriu Soltan

Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA, e-mail: lawrence@gmu.edu, e-mail: vsoltan@gmu.edu

Abstract: 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

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Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.

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