Timeline for Convergence of a product in $\mathbb Q_2[[X]]$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 24 at 8:37 | answer | added | KConrad | timeline score: 9 | |
| Apr 24 at 6:41 | comment | added | YCor | This lies in $\mathbf{Z}_2[\![X]\!]$, where there is a natural compact topology. | |
| Apr 24 at 6:40 | history | edited | YCor |
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| Apr 24 at 4:25 | comment | added | LSpice | Re, yes. | |
| Apr 24 at 4:01 | comment | added | joaopa | Thanks, product topology means convergence coefficient by coefficient, right? | |
| Apr 24 at 3:55 | comment | added | LSpice | Well, you can put any topology you like; it's your question. One possibility would be to equip $\mathbb Q_2[[X]]$ with the product topology coming from viewing it as a product of infinitely many copies of $\mathbb Q_2$. Is that what you want? | |
| Apr 24 at 3:54 | comment | added | joaopa | Is it possible? | |
| Apr 24 at 3:52 | comment | added | LSpice | But then the product can't possibly converge, because even the $X$ term never stabilises. So do you want a topology on $\mathbb Q_2[[X]]$ that takes into account the topology on $\mathbb Q_2$? | |
| Apr 24 at 3:51 | comment | added | joaopa | this one induced by the order of a formal power series: $F=\sum_{j\ge k}a_jX^j$ ($a_j\in\mathbb Q_2,\ a_k\ne0$), $\mathrm{ord}(F)=k$. | |
| Apr 24 at 3:50 | history | edited | LSpice | CC BY-SA 4.0 |
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| Apr 24 at 3:49 | comment | added | LSpice | What's the topology on $\mathbb Q_2[[X]]$? | |
| Apr 24 at 3:44 | history | asked | joaopa | CC BY-SA 4.0 |