In this quesiton it is mentioned that the algebra of smooth functions from a compact Manifold $M$ to a Frechet space $F$ is isomorphic to the projective tensor product $C^{\infty}(M) \otimes_\pi F$, i.e.
$$ C^{\infty}(M) \otimes_\pi F \cong C^{\infty}(M, F) $$
Do you have references to that result? Do I have to assume that $F$ is a Frechet space for this to hold, or does it hold for arbitrary locally convex vector spaces?