Convex Sets and Convex Combinations on Complex Linear Spaces

Let V be a non empty zero structure. An element of Cthe carrier of V is said to be a C-linear combination of V if: (Def. 1) There exists a finite subset T of V such that for every element v of V such that v / ∈ T holds it(v) = 0. Let V be a non empty additive loop structure and let L be an element of Cthe carrier of V . The support of L yielding a subset of V is defined by: (Def. 2) The support of L = {v ∈ V : L(v) 6= 0C}. Let V be a non empty additive loop structure and let L be a C-linear combination of V . One can check that the support of L is finite. The following proposition is true