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On Uniform Convergence

  1. Aug 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Just trying to get feel for uniform convergence and it's relationship to boundedness. If a sequence of functions (fn) converges uniformly to f and (fn) is a sequence of bounded functions, is f also bounded?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 6, 2007 #2


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    If the convergence is uniform then for all e there is an N such that |fn(x)-f(x)|<e for all n>=N. If fN is bounded and f unbounded, how can this be?
    Last edited: Aug 6, 2007
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