Uniform Continuity Proof for Periodic and Continuous Functions | Analysis Help

[kiriyama]

1. Prove if f:R->R is periodic and continuous, then f is uniformly continuous



2. There exists h that does not equal zero such that f(x+h)=f(x)

 

[matt grime]

Can you think of any results you know about conditions that make continuous functions into uniformly continuous ones?

 

[HallsofIvy]

For 1, I agree with matt grime, Think about theorems that say when a continuous function is uniformly continuous (on a given set of course- "uniform" continuity is always defined on a given set. You want to prove that this function is uniformly continuous on the set of all real numbers. Knowing the function is periodic means you can look at a finite interval!)

For 2, exactly what is the DEFINITION of "periodic"?