Timeline for Pullbacks and Inclusions of Smooth function algebras of manifolds.
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2012 at 3:49 | comment | added | Mark.Neuhaus | Ryan then I guess that you just didn't recognized that I didn't assumed the embedding to be closed. So the anser to my first question is no. | |
| May 2, 2012 at 1:37 | comment | added | Ryan Budney | The Urysohn lemma requires the submanifold to be closed, so it's no contradiction. | |
| May 2, 2012 at 0:38 | comment | added | Mark.Neuhaus | I'm a little confused because what Igor said seems to contradict what Ryan said since I do not assume that $i(M)$ is closed in $N$. | |
| Apr 27, 2012 at 6:58 | comment | added | Igor Khavkine | For the surjectivity question and important condition is that the image of $M$ be closed in $N$. Otherwise, if $M$ has an end, smooth functions on $M$ could have wild behavior as they approach that end and not correspond to the restriction of any smooth function from the ambient manifold $N$. Think $(0,1)$ in $\mathbb{R}$. | |
| Apr 26, 2012 at 21:21 | vote | accept | Mark.Neuhaus | ||
| May 2, 2012 at 0:39 | |||||
| Apr 26, 2012 at 21:20 | comment | added | Mark.Neuhaus | ok. Didn't see that it was that easy. So I vote for close to, since I don't want to delete it, just in case someone else is looking for the same thing in future. | |
| Apr 26, 2012 at 21:15 | history | answered | Ryan Budney | CC BY-SA 3.0 |