0
$\begingroup$

A set $C \in R^n$ is called convex if the line segment $L = \{ tp + (1-t)p | 0 \lt t \lt 1 \}$ between two arbitrary points $p,p' \in C$ is contained in $C$. The convex hull $CH(C)$ of a set $C \subset R^n$ is the intersection of all convex sets of $R^n$ containing $C$:$$CH(C)= \cap\{C' \subset R^n | C\subset C' , C' convex \} $$ prove that the convex hull is convex.

$\endgroup$

1 Answer 1

3
$\begingroup$

Pick 2 points in the convex hull. Then by def. Then every C' convex which contains C has the line segment between those points. Thus the intersection of all convex sets containing C has that line segment so the convex hull contains the lime segment

$\endgroup$
2
  • $\begingroup$ Thank you for the guidance. But I am not quiet sure I understood that well. Could you please explain more ? $\endgroup$
    – Erik
    Dec 1, 2014 at 16:24
  • 1
    $\begingroup$ Try spending more than 3 minutes thinking about it. $\endgroup$
    – Batman
    Dec 1, 2014 at 16:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.