$f_n \in C([0,1])$ is a sequence of functions. Why is the implication
$f_n$ converges to $f \in C([0,1])$ with respect to $||·||_1$ $\Rightarrow$ $f_n$ converges to $f$ with respect to $||·||_\infty$ wrong?
Well, i tried to do: For $\varepsilon>0$ there is $N$ so that for $n>N$ there is $||f_n-f||_1<\varepsilon$ to conclude the falseness, but i didn't find a solution.
So how to prove that this implication is not true?