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Pointwise bounded, uniformly continuous family of functions locally uniformly bounded

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f_n:[a,b] -> R be a pointwise bounded, continuous family. Prove there exists an interval (c,d) < [a,b] on which f_n is uniformly bounded.


    2. Relevant equations
    no equations


    3. The attempt at a solution
    I'm stuck. If we have equicontinuity, then this is easy, so i'm thinking we need to prove we have some kind of local equicontinuity or equicontinuity at one point, but I've not been successful in breaking through with these ideas. I don't have a hook!
     
  2. jcsd
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