I had following doubt 1) Why linear functional $\phi_x(f)=f(x)$ is continous ?
2)Why $D_k$ is closed in $C^\infty$? (I do not understand the intersection of null space argument
3) why $C^\infty $ is complete?I know that over compact set it is complete using uniform convergence but i do not understand reasioning as set is open?
Please help me to understand above question
Any Help will be appreciated