Timeline for Wanted: chain of nowhere dense subsets of the real line whose union is nonmeagre, or even contains intervals
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2011 at 0:21 | vote | accept | Michael | ||
| Jan 18, 2011 at 0:20 | answer | added | Nate Eldredge | timeline score: 3 | |
| Jan 18, 2011 at 0:18 | comment | added | George Lowther | @Joel: yes, sorry, that was a dumb mistake. Not sure about my second comment now | |
| Jan 18, 2011 at 0:15 | comment | added | Joel David Hamkins | George, I think you mean to say that under CH, the real line is the union of a chain of countable sets. (Every union of a chain of finite sets can be seen to be countable.) | |
| Jan 18, 2011 at 0:08 | comment | added | George Lowther | Assuming CH, the real line is a union of a chain of finite sets, since this is true for the first uncountable ordinal. So the answer is yes in that case. | |
| Jan 18, 2011 at 0:07 | answer | added | Joel David Hamkins | timeline score: 15 | |
| Jan 17, 2011 at 23:20 | comment | added | Michael | Andres, I do not see how this resolves my question. Although your set $T_\alpha$ is the union of a chain of sets with empty interior, this does not imply it is the union of a chain of nowhere dense sets. The rationals could very well precede $T_\alpha$ in your ordering but are certainly not nowhere dense. | |
| Jan 17, 2011 at 22:29 | history | asked | Michael | CC BY-SA 2.5 |