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Compact sets homework

  • Thread starter nicorette
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  • #1
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Homework Statement



X and Y are compact sets in R^n that are disjoint. Then there must be positive distance between the elements of these sets.


Homework Equations




The Attempt at a Solution



since X and Y are compact , X X Y is compact. Then, for the distance function d(x in X, y in Y): R^n X R^n -> R, there is a maximum and a minimum.

I think this should be a sufficient proof, although I'm not really sure how exactly to show that X X Y is compact as well.
 

Answers and Replies

  • #2
Dick
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You've got the right idea, but you haven't shown the minimum can't be zero. Have you? Do you need to show XxY is compact? Or it that something you already proved?
 
  • #3
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I don't know how to show the minimum can't be zero. So far as X x Y being compact, I just assumed, I don't know where to start for a proof

thanks a lot
 
  • #4
Dick
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Don't worry about proving XxY compact for the moment, concentrate on the first one. Suppose the distance is zero. How can that be?
 

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