Hello everyone, I was wondering if anyone knew how to prove that the map from $C^{\infty}(M)$ to $\xi (p)$, that is, from the infinitely differentiable functions on a manifold M to the space of (once)differentiable function germs, where the map is associating to each f in $C^{\infty}(M)$ its class in $\xi (p)$ is onto. By the way, since you ask, the reason I'm interested in this is because its a question that WAS on my final for differential topology, I've tried to work it out since then but no luck so far, this is not homework it's just curiosity now, hope its ok ill have to check the post regultaions, sorry, if not just tell me and i'll delete the question...
closed as offtopic by Ricardo Andrade, Andrey Rekalo, Olivier Benoist, Stefan Kohl, Willie Wong Nov 28 '13 at 12:46This question appears to be offtopic. The users who voted to close gave this specific reason:



I think your question is misstated, because this map is not onto: There is no smooth function on the reals whose germ at $0$ is the germ of $xx$, a oncedifferentiable function germ. Assuming this is not what you wanted, please restate the question, and include an explanation of why you are interested in it ;) 

