# C[0,2pi] separable?

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• February 27th 2013, 01:25 PM
BrownianMan
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.

Thanks
• March 10th 2013, 09:14 AM
hatsoff
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 $g(t)=f(t/2\pi)$.