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
