Timeline for Objects which can't be defined without making choices but which end up independent of the choice
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2016 at 13:03 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| May 21, 2013 at 2:03 | comment | added | Asaf Karagila♦ | David, yes. one takes a section over the image of $[0,1]$. But if the section accidentally ended up equal to the section taken over the image of $[0,\ln2]$? It could be equal to the section of $[3/\pi,1]$ too. These are sections which are isomorphic as sets, but we can still arrange for those sections to have different outer measure. So it all comes down to what sort of structure you care about preserving. | |
| May 21, 2013 at 1:03 | comment | added | David Roberts♦ | If you're thinking of the classical Vitali set, one is taking a section of $\mathbb{R} \to \mathbb{R}/\mathbb{Q}$ over the image of $[0,1]$. All such sections have isomorphic images as sets, but perhaps you were thinking of other Vitali sets. | |
| May 20, 2013 at 22:35 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |