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Math Help - C[0,2pi] separable?

  1. #1
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    C[0,2pi] separable?

    So I know how to prove that the space of all continuous functions in [0,1] is separable. But I was thinking, the space of real valued continuous functions which are periodic (with period 2pi) should also be separable. The prof didn't prove this (and I am not sure he will) but I am interested in seeing a proof nevertheless.

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  2. #2
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    Re: C[0,2pi] separable?

    Why not just build an isometric isomorphism between C[0,1] and C[0,2\pi]? Let f\in C[0,1]\mapsto g\in C[0,2\pi] be defined by g(t)=f(t/2\pi).
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