1
$\begingroup$

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

  • 0
    $\{X\setminus P\}_{P\in B}$ is an open cover of $X$.2012-10-18

1 Answers 1