Definition 2

Let C be a convex cone of vertex 0 in a vector space E. We say that a half-line D ⊂ C originating at 0 is an extremal generator of C, if every open segment contained in C, not containing 0 and meeting D is contained in D.

It comes to the same thing to say that for all x ∈ D such that x ≠ 0, if y ≠ 0, y' ≠ 0 are two points of C such that x = y + y', then, it is necessarily the case that y ∈ D and y' ∈ D.