# characteristic function of the rationals [duplicate]

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 $\chi$?

-

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

This question was marked as an exact duplicate of an existing question.

– Jonas Meyer Sep 15 '11 at 3:54
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