Timeline for Reference for working with the implicit function theorem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2019 at 15:28 | vote | accept | David E Speyer | ||
| Nov 12, 2019 at 16:50 | comment | added | David E Speyer | Thanks! This looks nice. I may try this out next time I teach our honors calculus on manifolds course. | |
| Nov 12, 2019 at 16:10 | comment | added | Tobias Diez | Sure, this particular statement follows from the rank theorem. If I understood @David E Speyer correctly, he wanted to have a general theorem/treatment of various applications of the inverse function theorem, and this is what this abstract normal theorem provides. The singular part $f_s$ is of course only important if you work with submersions/constant rank maps. | |
| Nov 12, 2019 at 15:51 | comment | added | Ben McKay | You might just use the usual rank theorem to say that $(x_1,\dots,x_{n-1},f)$ are local coordinates, so can just write them as $(x_1,\dots,x_{n-1},x_n)$, and then $(x_n=0)$ has coordinates $x_1,\dots,x_{n-1}$. I don't see why you need to worry about $f_s$, and without $f_s$, this is just the usual rank theorem. | |
| Nov 12, 2019 at 14:53 | history | answered | Tobias Diez | CC BY-SA 4.0 |