
Journal of Convex Analysis 16 (2009), No. 3, 749766 Copyright Heldermann Verlag 2009 When is a Convex Cone the Cone of all the HalfLines Contained in a Convex Set? Emil Ernst Université de AixMarseille, UMR6632, 13397 Marseille, France Emil.Ernst@univcezanne.fr Michel Volle Université d'Avignon et des Pays de Vaucluse, 74 Rue Louis Pasteur, 84029 Avignon, France Michel.Volle@univavignon.fr We prove that every convex cone V of a real vector space X possessing an uncountable Hamel basis may be expressed as the cone of all the halflines contained within some convex subset C of X (in other words, V is the infinity cone to C). This property does not hold for lowerdimensional vector spaces; more precisely, a convex cone V in a vector space X with a denumerable basis is the infinity cone to some convex subset of X if and only if V is the union of a countable ascending sequence of linearly closed cones, while a convex cone V in a finitedimensional vector space X is the infinity cone to some convex subset of X if and only if V is linearly closed. Keywords: Infinity cone, recession analysis, spreading cover. MSC: 26B99, 46N10, 49J99 [ Fulltextpdf (162 KB)] for subscribers only. 