Timeline for A version of implicit function theorem when sections are not everywhere smooth?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 14, 2013 at 18:18 | comment | added | Peter Michor | @Ritwik: Weak means, that the implicitly given function is just strictly differentiable at each point of $s_1^{−1}(0)$. This means $lim_{x≠y→x_0}\frac{f(x)−f(y)}{x−y}$ exists (1-dim version). | |
| Jun 14, 2013 at 16:23 | vote | accept | Ritwik | ||
| Jun 14, 2013 at 13:15 | comment | added | Ritwik | Thank you, this seems to be a very clear counter example. Regarding your second comment, suppose I assume that $s_2:M \rightarrow V_2$ is smooth. Does that mean the answer to my question is yes? Or do I have to modify the question slightly? You said it's true in some weak sense. Usually that means that I have to have a different notion of what it means to have a solution. | |
| Jun 14, 2013 at 12:24 | history | answered | Peter Michor | CC BY-SA 3.0 |