Abstract
We give a few results about the separation of two convex polyhedra in an arbitrary real vector space; so we generalize theorems of Černikov, Klee, Rockafellar and Gallivan-Zaks.
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Bair J.: A propos d'un problème de Klee sur la séparation de plusieurs ensembles, en voie de publication dansMath. Scand.
Bair J. - Fourneau R.:Etude géométrique des espaces vectoriels — une introduction, Lect. Notes in Math., vol. 48 9, Springer-Verlag, Berlin-Heidelberg-New-York, 1975.
Bair J. - Fourneau R.: Caractérisation de polyèdres convexes et systèmes d'inéquations linéaires, en voie de publication dansBull. Soc. Roy. Sc. Liège.
Bair J. - Jongmans F.: Séparation franche dans un espace vectoriel,Bull. Soc. Roy. Sc. Liège, 39 (1970), 474–477.
Bair J. - Jongmans F.: La séparation vraie dans un espace vectoriel,Bull. Soc. Roy. Sc. Liège, 41 (1972), 163–170.
Černikov S.N.: Theorems on the separability of convex polyhedral sets,Soviet Math.,Doklady, 136–138 (1961), 838–840.
Gallivan S. - Zaks J.: Replacing convex sets by polytopes, à paraître.
Grunbaum B.:Convex polytopes, Interscience publishers, 1967.
Klee V.: Separation and support properties of convex sets — a survey, inBalakrishnan, Control theory and the calculus of variations, Acad. Press, New-York, 1969.
Rockafellar R.T.:Convex analysis, Princeton University Press, 1970.
Roy A.K.: Facial structure of the sum of two compact convex sets,Math. Annalen, 197 (1972), 189–196.
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Bair, J. Criteres de separation pour polyedres convexes. J Geom 10, 17–31 (1977). https://doi.org/10.1007/BF01933059
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DOI: https://doi.org/10.1007/BF01933059