1. ## 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 $\bigcap_{i=1}^n X_i\neq \emptyset$.

2. that is related with the Helly's theorem, I found it on the web, so forgot that question.

3. Originally Posted by Andres Perez
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

4. 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.