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Nested sequence of compact sets in Rn has a non-empty intersection?

  1. Mar 3, 2009 #1
    There's a theorem that says any nested sequence of compact sets in Rn always has a non-empty intersection. So there is something wrong with this counterexample. I'm not able to see what's wrong:

    Consider the interval Un = [2-1/n, 1+1/n] for n=1, 2 and 3.
    Isn't the intersection of U1, U2 and U3 the null set? (since U3 is the null set?)
  2. jcsd
  3. Mar 4, 2009 #2


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    There is a theorem that say any nested sequence of non-empty compact sets in Rn is has non-empty intersection.
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