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Uniform convergence question

  1. Jun 10, 2010 #1
    Let [tex] y_n [/tex] be a sequence of functions in [tex] \mathcal{C}([0,1], \mathbb{R}) [/tex]
    Suppose that every subsequence of [tex] y_n [/tex] has a subsequence that converges uniformly. Prove that they all converge to the same limit.
  2. jcsd
  3. Jun 10, 2010 #2


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    Science Advisor

    So, what have you tried?
  4. Jun 10, 2010 #3
    This is not an exercise. This is a question that rose solving an exercise. Can't solve it.
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