Strictly convex set

Summary

A strictly convex set is a convex set in which the open segment between any two distinct points lies in the interior of the set. Its boundary contains no flat piece: no nontrivial segment lies on the boundary. A normed space is a strictly convex space exactly when its closed unit ball is a strictly convex set. Strict convexity gives uniqueness, for example of the point of a set where a nonzero linear function is largest.