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.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top