I'm having trouble understanding the definition of convex hull. Can somebody give me an example? For example if I have the real convex set $(a,b)$ then what is its convex hull? Is it $(a,b)$ or is it $[a,b]$?
Does convex hull of convex set $S$ always equal the convex set $S$ itself? If not, example?
Thank you for any help =)
Convex hull of $A$ is, by definition, the smallest* convex set which contains $A$.
So the convex hull of $(a,b)$, which is already convex by the way, is obviously $(a,b)$.
Similarly, convex hull of any convex set $S$ must be $S$, by definition.
*smallest: Smallest here means that the convex hull is the intersection of all convex sets containing $A$.