Geodesic
Separability of H-convex Sets
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 131-137 Cet article a éte moissonné depuis la source Heldermann Verlag

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We consider the problem of H-separability for two H-convex subsets A and B of Rn. There are two types of H-separability. The first one, called "strict H-separability", is the separation (in the usual sense) of the sets A and B by an H-convex hyperplane. The second one ("weak H-separability") means to look for an H-convex half-space 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 H-separability; the results are connected to the H-convexity of the Minkowski sum of H-convex sets investigated in a previous paper of the authors [J. Combin. Theory, Ser. A 103 (2003) 323--336]. Some examples illustrate the obtained results.
Classification : 52A01, 52A20
Mots-clés : Convex sets, H-convexity, Minkowski addition, separation theory 
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     author = {V. Boltyanski and H. Martini},
     title = {Separability of {H-convex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {131--137},
     year = {2005},
     volume = {12},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a7/}
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V. Boltyanski; H. Martini. Separability of H-convex Sets. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 131-137. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a7/