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

Homework Help: Proving question

  1. Oct 2, 2005 #1
    I need help with this question which askes to prove it. Anyone has any idea?

    If [tex]\text C_{1} , C_{2} , C_{3}[/tex] , … are all closed sets in [tex]\text R^n[/tex] , then the set [tex]\text c = I_{k=1}^{\infty}c_{k} [/tex] is also a closed set in [tex]\text R^n[/tex] .
  2. jcsd
  3. Oct 2, 2005 #2
    What is I ?
  4. Oct 2, 2005 #3
    You want to show that the intersection contains all of its limit points. Try letting z be in cl(C), the closure of C, such that a sequence {z_n} in C converges to z. Then show that z must be in C.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook