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Homework Help: Uniform continuity and bounds

  1. Nov 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that if a function f:(0,1) --> lR is uniformly continuous, f is bounded.

    2. Relevant equations

    3. The attempt at a solution

    Really don´t know. I started thinking about Weierstrass Thereom but I am not sure that it´s ok. Now I think that may be is something about the properties of uniform continuities. Any help would be great.

    Thanks in advance.
  2. jcsd
  3. Nov 5, 2008 #2


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    Science Advisor
    Homework Helper

    This is an easy epsilon-delta argument. Work with the definition of uniform continuity. (It's always helpful to draw a picture.)
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