Let $X$ be a compact set. Suppose $V$ be a collection of set of closed set $P$ where each $P$ are closed set in $X$ and any intersection of finite subcollection of $V$ is nonempty. then $\bigcap_{P\in V} P$ is also non empty. I tried to use contradiction to prove it but cannot get a contradiction. Any method is fine. Thx
A question about intersection of closed set is non empty
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general-topology
compactness
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0$\{X\setminus P\}_{P\in B}$ is an open cover of $X$. – 2012-10-18