# continuous and Periodic function is Uniformly continuous [duplicate]

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

Thank you!

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## marked as duplicate by Normal Human, ronno, Peter Woolfitt, RecklessReckoner, quidMay 17 at 20:45

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 $\mathbb R$.