Could you please prove or disprove both:
(a) The convex hull of a closed set is closed
(b) The convex hull of a compact set is compact.
(b) I'm assuming that in your textbook you have a theorem (usually called the Cartheodory Theorem) which states that:
"For a set C <> 0 (empty set) in R^n, evern point of the convex hull of C belongs to some simplex with vertices in C and thus can be expressed as a convex combination of n+1 points ...
Convex Hulls, Closed and Compact Sets are investigated using the Cartheodory Theorem. The solution is well explained.