# Convex Hull : Closed and Compact Sets

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

https://brainmass.com/math/geometry-and-topology/convex-hull-closed-compact-sets-27528

#### Solution Preview

(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 ...

#### Solution Summary

Convex Hulls, Closed and Compact Sets are investigated using the Cartheodory Theorem. The solution is well explained.

$2.49