Let $C[a,b]$ be the space of all continuous functions on $[a, b]$. For each $x\in [a,b]$ the map $E_{x}(f)=f(x)$ is a map from $C[a,b]$ to $R$ called the evaluation map. Prove that the weak topology generated by $\{e_{x} : x\in [a,b]\}$ is same as the topology of pointwise convergence on $C[a,b]$.
What is the difference between weak topology generated by $\{e_{x} : x\in [a,b]\}$ and is same as the topology of pointwise convergence on $C[a,b]$? some ideas for this excercise?