Timeline for Everywhere differentiable function that is nowhere monotonic
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2021 at 6:57 | comment | added | Fedor Petrov | Ah, thank you. I thought it is $F_\sigma$ (since irrationals are $G_\delta$ but can not be a zero set of a derivative), but indeed it is $G_\delta$ for any Baire class one function. | |
| Oct 29, 2021 at 22:21 | comment | added | Pietro Majer | The zero-set of a derivative is always $G_\delta$ set, and for these functions is also dense. An intersection of countable many dense $G_\delta $ sets of $\mathbb R$ is a dense $G_\delta$ by the Baire theorem. So a sequence of such functions always have a common $G_\delta$ set of zeros. | |
| Oct 29, 2021 at 21:56 | comment | added | Fedor Petrov | Why does a uniform limit of such functions have a dense set of zeroes? | |
| Oct 29, 2021 at 20:29 | history | answered | Pietro Majer | CC BY-SA 4.0 |