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

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* Corresponding author 1 LATP - Laboratoire d-Analyse, Topologie, Probabilités 2 LANLG - Laboratoire d-Analyse non linéaire et Géométrie

Abstract : 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.

Keywords : infinity cone recession analysis spreading cover

Author: ** Emil Ernst - Michel Volle - **

Source: https://hal.archives-ouvertes.fr/