Timeline for Is $\mathcal{P}(\omega)/(fin)$ with the interval topology path-connected?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Nov 8, 2017 at 20:37 | comment | added | Joel David Hamkins | Well, further consideration shows that this is not a path after all, and I now expect that this space is not path-connected. | |
| Nov 8, 2017 at 19:15 | comment | added | Dominic van der Zypen | That would be great @JoelDavidHamkins, this has been open for some time. Thanks in advance for your effort! | |
| Nov 8, 2017 at 18:45 | comment | added | Joel David Hamkins | It seems to me that it is; I'll write up something later when I have a chance. | |
| Nov 8, 2017 at 17:02 | comment | added | Joel David Hamkins | If we use $J=\mathbb{Q}\cap[0,1]$ in place of $\omega$, is the map from the unit interval $x\in[0,1]$ to the rational cut $\{q\in J\mid q<x\}$ a path from $\emptyset$ to $J$ in $P(J)/\text{Fin}$? If so, then we could translate this all around and path-connect any point to the top, deducing path-connectedness of $P(\omega)/\text{Fin}$. That is, we basically map reals to their cut in the rationals. Is it a path? | |
| Nov 8, 2017 at 10:45 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
included definition of interval topology
|
| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Mar 30, 2015 at 17:57 | comment | added | Nik Weaver | Oh, I misread the definition, sorry. | |
| Mar 30, 2015 at 15:36 | comment | added | Dominic van der Zypen | No, otherwise $\mathcal{P}(\omega)/fin$ would be disconnected, but it is connected (see mathoverflow.net/questions/200784/… ). My question is if it is even path-connected | |
| Mar 30, 2015 at 14:36 | comment | added | Nik Weaver | According to your definition of "interval topology", it looks as though every subbasic open set is also closed, in any poset ... | |
| Mar 30, 2015 at 13:28 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
edited title
|
| Mar 30, 2015 at 13:27 | history | undeleted | Dominic van der Zypen | ||
| Mar 25, 2015 at 9:46 | history | deleted | Dominic van der Zypen | via Vote | |
| Mar 25, 2015 at 9:44 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |