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Article Dans Une Revue Journal of Convex Analysis Année : 2009

When is a convex cone the cone of all the half-lines contained in a convex set?

Résumé

In this article 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.
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Dates et versions

hal-00819389 , version 1 (01-05-2013)

Identifiants

  • HAL Id : hal-00819389 , version 1

Citer

Emil Ernst, Michel Volle. When is a convex cone the cone of all the half-lines contained in a convex set?. Journal of Convex Analysis, 2009, 16 (3), pp.749-766. ⟨hal-00819389⟩
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