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Math Help - About convex open sets

  1. #1
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    About convex open sets

    Let X_1,\ldots ,X_n\subseteq \mathbb{R}^m be convex open sets such that X_i\cap X_j\cap X_k\neq \emptyset for every i,j,k. Show that \bigcap_{i=1}^n X_i\neq \emptyset.
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  2. #2
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    that is related with the Helly's theorem, I found it on the web, so forgot that question.
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  3. #3
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    Quote Originally Posted by Andres Perez View Post
    that is related with the Helly's theorem, I found it on the web, so forgot that question.
    Why don't you share it with the rest of us. It might help someone else.

    -Dan
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  4. #4
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    you can find a proof on Helly's theorem - Wikipedia, the free encyclopedia but it is a special case. i don't know if the statement i wrote is true. The question is open.
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