Can there be a convex hull for a non-convex set?

Question

Is it necessary that convex hulls can exist only for convex sets or can it exist for non-convex sets too? For example, see the picture here (Don't have enough reputation to post images). The left set is convex, and the convex hull is the set itself. But the set on the right is a non-convex set. Can there exist a convex hull for it?

Answer 1

A convex hull is defined for any set, and in fact, it's only really interesting when the set is not convex. If it is already convex, then the convex hull is itself, because the convex hull is defined as the smallest convex set that contains the set.

In contrast, the convex hull of the picture on the right is just all points that are on any segment between any two points of the U. So everything on the line that's drawn is in the convex hull, along with any similarly drawn line.