Timeline for Pullbacks and Inclusions of Smooth function algebras of manifolds.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2012 at 9:21 | comment | added | Neil Strickland | One can show that any $\mathbb{R}$-algebra homomorphism $C^\infty(M)\to\mathbb{R}$ has the form $f\mapsto f(x)$ for a unique point $x\in M$. Using this one can deduce that the functor $C^\infty(-)$ gives a full and faithful contravariant embedding of smooth manifolds in $\mathbb{R}$-algebras. This does not answer the question, but it is illuminating background. | |
| Apr 26, 2012 at 21:21 | vote | accept | Mark.Neuhaus | ||
| May 2, 2012 at 0:39 | |||||
| Apr 26, 2012 at 21:15 | comment | added | MTS | Mark, while this is a good question, it is not really research level. The second question is essentially trivial, while the first question is asking if all smooth functions on an embedded submanifold can be extended to the ambient manifold. I suggest looking at a differential geometry book such as Lee's Introduction to Smooth Manifolds - if you can't find what you're looking for there, try math.stackexchange.com I am voting to close. | |
| Apr 26, 2012 at 21:15 | answer | added | Ryan Budney | timeline score: 3 | |
| Apr 26, 2012 at 20:17 | history | asked | Mark.Neuhaus | CC BY-SA 3.0 |