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- #1

- Jan 17, 2013

- 1,667

If \(\displaystyle \mathbb{K}_{\alpha}\) is a collection of compact subsets of a metric space \(\displaystyle X\) such that the intersection of every finite sub collection of \(\displaystyle \mathbb{K}_{\alpha}\) is nonempty , then \(\displaystyle \cap\, \mathbb{K}_{\alpha} \) is nonempty .

If I understand correctly then this theorem states that if any finite intersection is nonempty then any arbitrarily intersection is also nonempty , right ?. I was trying to understand the proof but it wasn't so clear for me .