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∞(M) is denoted by E′ and the space of all linear functional on C∞0(M) is denoted by D′.

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