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Let $\chi$ be the characteristic function of the rational numbers in $[0,1]$. Does there exist a sequence $\{f_n\}$ of continuous functions on $[0,1]$ that converges pointwise to $\chi$?

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marked as duplicate by Lord_Farin, rschwieb, Amzoti, Martin, azimut Jun 21 '13 at 12:41

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The characteristic function is a classic example of the Baire class 2 en.wikipedia.org/wiki/Baire_function. –  Andrew Sep 15 '11 at 5:30
Good questions here should have two additional pieces of information: where you encountered the problem, and what you have already tried. –  Carl Mummert Sep 15 '11 at 10:56

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