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Title: Support and separation properties of convex sets infinite dimension
Authors: Soltan, V.
Keywords: Convex;Cone;Bound;Hyperplane;Support;Separation;Convexo;Cono;Ligado;Hiperplano;Soporte;Separación
Issue Date: 2021
Publisher: Universidad de Extremadura, Servicio de Publicaciones
Abstract: This is a survey on support and separation properties of convex sets in the n-dimensional Euclidean space. It contains a detailed account of existing results, given either chronologically or in related groups, and exhibits them in a uniform way, including terminology and notation. We first discuss classical Minkowski's theorems on support and separation of convex bodies, and next describe various generalizations of these results to the case of arbitrary convex sets, which concern bounding and asymptotic hyperplanes, and various types of separation by hyperplanes, slabs, and complementary convex sets.
ISSN: 0213-8743
DOI: 10.17398/2605-5686.36.2.241
Appears in Collections:Extracta Mathematicae Vol. 36, nº 2 (2021)

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