Convex Hull, Set of Convex Combinations and Convex Cone
نویسندگان
چکیده
Let V be a real linear space. The functor ConvexComb(V ) yielding a set is defined by: (Def. 1) For every set L holds L ∈ ConvexComb(V ) iff L is a convex combination of V . Let V be a real linear space and let M be a non empty subset of V . The functor ConvexComb(M) yielding a set is defined as follows: (Def. 2) For every set L holds L ∈ ConvexComb(M) iff L is a convex combination of M . We now state several propositions: (1) Let V be a real linear space and v be a vector of V . Then there exists a convex combination L of V such that ∑ L = v and for every non empty subset A of V such that v ∈ A holds L is a convex combination of A.
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