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Question: prove that c 0 1 ii i is not...

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. Prove that (C ([0, 1]), II. I) is not complete by building a Cauchy sequence (fn) C C1([0,1]) that does not converge to a C1(00, 11) function in the Loo norm (no need to write analytical formulas, a good picture would be enough) In fact, by the Stone-Weierstrass theorem, we know that Cr([0, 1])11-llao. = Co([0, 1]) for any r 0, 1,2,.., oo, w since every continuous function is the uniform limit of a sequence of polynomials.
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