Show that the convex hull of a set $S$ is the intersection of all convex sets that contain $S$. Suppose $H$ is the convex hull of $S$, and $D$ is the intersection of all convex sets contain $S$. Certainly, it's easy to prove that $H \subset D$, but how to prove that $D \subset H$?
Asked
Active
Viewed 1,804 times
1
-
What definition of convex hull are you using? – coffeemath Apr 01 '18 at 08:48
-
The definition : the set of all convex combinations of points in $C$ – Tsuong.S Apr 01 '18 at 08:54
-
Do you know that the convex hull is itself a convex set? (This is a simple verification). If you kn ow this it is obvious that $D \subset H$. – Kavi Rama Murthy Apr 01 '18 at 12:16
-
I get it!Thanks!! – Tsuong.S Apr 01 '18 at 14:39