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Convex Hull : Closed and Compact Sets

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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.

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Solution Summary

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

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(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 ...

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