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Convexity of a set

  1. Jan 15, 2012 #1
    A set is convex if it's additive and divisible. To find out the convexity you just pick any two points and draw a tangent line. If the line lies within the area - voila, the set is convex. Similarly, if the set is nonconvex, you just show that a part of any tangent line can lay outside of the set.

    But in the case of nonconvexity, how do I show that it is also nonadditive and nondivisible?

    I've got a set that looks like a flat donut where the donut hole is not a part of the set. I already showed that the set is nonconvex by drawing a tangent line. I do struggle to show (without complex proofs), that the set is also nondivisible and nonadditive.

    Any help is greatly appreciated.
  2. jcsd
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