Reference no: EM131582656

Question: Show that a point xi in a convex set X is a relative interior point of X if and only if either of the two following (equivalent) conditions holds:

(i) For any line L in aff X, with xi ∈ L, there exist points x'; and x" in L ∩ aff X such that xt ∈ (x' x").

(ii) For any point x'; ∈ X, with x'; ≠ xi there is a point x" ∈ X such that xi ∈ (x' x"). That is, the segment [x', y] in X can be extended beyond xi without leaving the set.