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Let $P,M$ and $N$ are smooth manifolds and let $F:P\times M \to N$ be a smooth map. We know its associated map $\tilde F:P \to C^\infty(M,N)$ given by $p \mapsto F_p(m)$ is continuous if and only if $F$ is continuous whenever we equip $C^\infty(M,N)$ with the weak topology. However this is not true in genreal if $C^\infty$ comes with the the strong (Whitney) topology; I feel the counterexample should not be that hard but I am unable to find it. Does anybody know such a function? Thanks in advance.

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