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 P: 58 I'm stuck ... Ive proved the intersection of any number of closed sets is closed ... and Let S = { A_a : a Element of I } be an collection of compact sets...then by heine Borel Theorem ...Each A_a in S is closed...so this part is done now I just have to show the intersection is bounded... so I said since each A_a in S is bounded by Heine Borel ..then A_a is a subset of [a,b] and then this is when Im really stuck: Let B={[a,b] : There exists an A_a in S such that A_a subset of [a,b]} I took the intersection of both sides of the subset ...and said Intersection S is a subset of Intersection of [a,b] so Intersection of S is bounded and therefore compact but somehow I think this is an error ..I dont know how to do this formally Please help