Question: Let $(X, mathcal{0})$ be compact, $U subseteq X$ open in $X$ and $$ mathcal{C}=left{C_{i} subset X mid C_{i} text { closed in } x forall

$Let $(X, \mathcal{0})$ be compact, $U \subseteq X$ open in $X$$

Let $(X, \mathcal{0})$ be compact, $U \subseteq X$ open in $X$ and $$ \mathcal{C}=\left\{C_{i} \subset X \mid C_{i} \text { closed in } x \forall i \in I ight\} $$ be such that $$ \bigcap_{i \in I} C_{i} \subset U $$ Show that there exists a finite number of closed sets $C_{i}$ such that its intersection is contained in $U$. CS.JG.136

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