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Given continuous and Periodic function, How can I prove that it is Uniformly continuous?

Thank you!

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2 Answers

up vote 4 down vote accepted

Observe that it is uniformly continuous when restricted to a closed interval whose length is a period of your function (or twice that, to simplify things a little bit), and then use periodicity to extend to the whole of $\mathbb R$.

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This is a hint... It is really not hard to do what you want. If you extend your question with details about what you have already tried or done, then it would probably be easier to help you. –  Mariano Suárez-Alvarez Mar 3 '11 at 15:25
    
Thank you for the comment.. I tried to use cantor theroem on [0,T] interval, and play a little bit with the definition using delta and epsilon, for any random x1 and x2 on R, Didn't manage to complete the proof. –  user6163 Mar 3 '11 at 15:31
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@Nir: I would really suggest that you play more with it before someone posts a complete solution... –  Mariano Suárez-Alvarez Mar 3 '11 at 15:48
    
:) o.k I'm going to play. –  user6163 Mar 3 '11 at 15:54
    
game is over.. Can't do that. –  user6163 Mar 3 '11 at 18:41
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a proof by contradiction but you should do it yourself!

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