In the proof of Stone-Weierstrass theorem provided in Rudin's Principles of Mathematical Analysis, why do we only need to show that there exists a sequence of polynomials $P_n$ that converges uniformly to the continuous complex function on $[0,1]$?
Stone-Weierstrass Theorem
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analysis
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0Could you please elaborate a little? Maybe give the precise statement of the conclusion and say why you don't see how it follows? – 2010-11-16
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0Because you can stretch it and so on? – 2010-11-16