Timeline for Short exact sequences every mathematician should know
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2021 at 17:30 | comment | added | Jan Bohr | On $M=\mathbb{R}$ we take $x(t)=t$, such that $X=\{0\}$. Now, if a smooth function $f:\mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(0)=0$, then by exactness of the SES we can write $f(t)=t g(t)$ for another smooth function $g:\mathbb{R}\rightarrow \mathbb{R}$. Inductively, if $f(t)=O(t^k)$, then $f(t) = t^k g(t)$ for a smooth function $g:\mathbb{R}\rightarrow\mathbb{R}$. This applies to the remainder in the Taylor series, where $g$ might a priori only be bounded. | |
| Mar 24, 2021 at 21:53 | comment | added | Zach Teitler | Can you please expand a bit on how the $M=\mathbb{R}$ case corresponds to remainders in Taylor series? | |
| S Aug 25, 2020 at 10:38 | history | answered | Jan Bohr | CC BY-SA 4.0 | |
| S Aug 25, 2020 at 10:38 | history | made wiki | Post Made Community Wiki by Jan Bohr |