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Homework Help: Prove that countable intersections of closed subset of R^d are closed

  1. Jan 3, 2010 #1
    Prove that countable intersections of closed subset of R^d are closed
     
  2. jcsd
  3. Jan 4, 2010 #2
    Try proving that countable unions of open subsets of R^d are open.
     
  4. Jan 4, 2010 #3
    If the intersection is not empty (what happens if it is?), consider a convergent sequence x(n) in it; what must happen to the limit? (Remember that closed sets must contain the limits of their convergent sequences).
     
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