Convex independence

Summary

A family of points is convexly independent if no point of the family lies in the convex hull of the other points. A set of points with this property is said to be in convex position. Then every point of the set is an extreme point of its convex hull. The notion is the convex analogue of linear and affine independence, and it is central in problems such as the Erdős–Szekeres problem on convex polygons.