## Exists continuous $f_n: 0,1 \to \mathbb{R}$ that converges pointwise, as $n \to \infty$, to $\chi_\mathbb{Q}$ November 29

Does there exist a sequence of continuous $f_n: [0, 1] \to \mathbb{R}$ that converges pointwise, as $n \to \infty$, to $\chi_\mathbb{Q}$, the characteristic function of the rationals in $[0, 1]$?