I have read definitions in my PDE book as follows: If $M$ is a smooth paracompact manifold, the space of all linear functional on $C^\infty(M)$ is denoted by $E'$ and the space of all linear functional on $C^\infty_0(M)$ is denoted by $D'$.

I have already known the topologies of these 4 spaces when $M$ is $R^n$, can you give me the general description of the topologies of these spaces?