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Topic: intersection of compact sets
Replies: 9   Last Post: Mar 30, 2005 2:56 AM

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Lawrence House

Posts: 76
Registered: 12/6/04
Re: intersection of compact sets
Posted: Mar 26, 2005 10:42 PM
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This seems complicated to me. In general a compact set is one that has the property that any open covering of it can be reduced to a finite subcovering. In Rn however it is simpler-i.e. a compact set is any set which is closed and bounded. A theorem says this. Furthermore an arbitrary intersection of closed sets is closed and so an arbitrary intersection of compact sets is compact. ( I think this is true in any topological space not just Rn.) So from this we have that the intersection of F(a) for every a is a closed subset of the open set G. But I don't know where to go from here. I'll keep trying.

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