would any one tell me whether $C[0,1]$ is complete under these metrics
1.sup norm i mean $\|f\|_{\infty}$
2.$\|f\|_{\infty,1/2}=\|f\|_{\infty}+|f(1/2)|$
3.$\|f\|_{2}=\sqrt{\int_0^1|f|^2dx}$
Under supnorm I know it is complete,I am not sure about the other two.