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Gerald Edgar
Gerald Edgar
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I have read definitions in my PDE book as follows: If M$M$ is a smooth paracompact manifold, the space of all linear functional on C∞(M)$C^\infty(M)$ is denoted by E′$E'$ and the space of all linear functional on C∞0(M)$C^\infty_0(M)$ is denoted by D′$D'$.

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

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?

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?

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Adterram
Adterram
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The topology of $C_0^\infty(M) $

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?