Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    There is a theorem that say any nested sequence of non-empty compact sets in Rn is has non-empty intersection.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Nested sequence of compact sets in Rn has a non-empty intersection?
Loading...