Geodesic
When is a Convex Cone the Cone of all the Half-Lines Contained in a Convex Set?
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 749-766

Voir la notice de l'article provenant de la source Heldermann Verlag

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 half-lines contained within some convex subset C of X (in other words, V is the infinity cone to C). This property does not hold for lower-dimensional 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 finite-dimensional vector space X is the infinity cone to some convex subset of X if and only if V is linearly closed.
Classification : 26B99, 46N10, 49J99
Mots-clés : Infinity cone, recession analysis, spreading cover 
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     author = {E. Ernst and M. Volle},
     title = {When is a {Convex} {Cone} the {Cone} of all the {Half-Lines} {Contained} in a {Convex} {Set?}},
     journal = {Journal of convex analysis},
     pages = {749--766},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a10/}
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E. Ernst; M. Volle. When is a Convex Cone the Cone of all the Half-Lines Contained in a Convex Set?. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 749-766. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a10/