
Journal of Convex Analysis 12 (2005), No. 1, 131137 Copyright Heldermann Verlag 2005 Separability of Hconvex Sets V. Boltyanski CIMAT, A.P. 402, 36000 Guanajuato, Gto., Mexico boltian@cimat.mx H. Martini Faculty of Mathematics, Technical University, 09107 Chemnitz, Germany martini@mathematik.tuchemnitz.de We consider the problem of Hseparability for two Hconvex subsets A and B of R^{n}. There are two types of Hseparability. The first one, called "strict Hseparability", is the separation (in the usual sense) of the sets A and B by an Hconvex hyperplane. The second one ("weak Hseparability") means to look for an Hconvex halfspace P such that A is situated in P, whereas B has no point in common with the interior of P. We give necessary and sufficient conditions for both these types of Hseparability; the results are connected to the Hconvexity of the Minkowski sum of Hconvex sets investigated in a previous paper of the authors [J. Combin. Theory, Ser. A 103 (2003) 323336]. Some examples illustrate the obtained results. Keywords: Convex sets, Hconvexity, Minkowski addition, separation theory. MSC: 52A01; 52A20 [ Fulltextpdf (244 KB)] for subscribers only. 