# projective tensor product of smooth functions

Let $M$ and $N$ be compact smooth manifolds. Is it true, that $C^{\infty}(M) \otimes_{\pi} C^{\infty}(N) \cong C^{\infty}(M \times N)$ as topological vectorspaces if endowed with the familiy of seminorms given by the suprema of differentials of the function over the respective spaces? If yes, is there a reference or easy explanation for this?

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