Differentiable function germs on differentiable manifolds - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T12:00:58Z http://mathoverflow.net/feeds/question/7933 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/7933/differentiable-function-germs-on-differentiable-manifolds Differentiable function germs on differentiable manifolds unknown (yahoo) 2009-12-06T00:26:10Z 2009-12-06T01:17:05Z <p>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...</p> http://mathoverflow.net/questions/7933/differentiable-function-germs-on-differentiable-manifolds/7935#7935 Answer by Andrew Critch for Differentiable function germs on differentiable manifolds Andrew Critch 2009-12-06T00:38:23Z 2009-12-06T00:38:23Z <p>I think your question is mis-stated, because this map is not onto:</p> <p>There is no smooth function on the reals whose germ at $0$ is the germ of $x|x|$, a once-differentiable function germ.</p> <p>Assuming this is not what you wanted, please restate the question, and include an explanation of why you are interested in it ;)</p>