Solution
= Solution
<Uniform convergence> means that for every $\varepsilon>0$ there is an integer $N$, independent of $x$, such that $|F_n(x)-F(x)|<\varepsilon$ for all $n\geq N$ and every $x\in(0,1)$. Equivalently $\sup_{0<x<1}|F_n(x)-F(x)|\to0$. In <pointwise convergence>, the required $N$ may depend on the chosen $x$.