Timeline for Largest Hausdorff quotient
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 15, 2011 at 14:32 | vote | accept | mbasic | ||
| Oct 15, 2011 at 14:32 | comment | added | mbasic | Thanks, Marino! I was thinking in the way you describe in your second post and got stuck once I saw that the result is not Hausdorff. :) | |
| Oct 15, 2011 at 3:03 | comment | added | Mariano Suárez-Álvarez | @Daniel, that is why I restricted to surjective maps. (In any case, the relation is well-defined even if one considers all maps and all $T_2$ sets, and one can easily show that there is a least topology satisfying the condition. One can quantify over all spaces!) | |
| Oct 15, 2011 at 2:59 | comment | added | Daniel Litt | There are some set-theoretic issues here, though they can be dealt with. (You are currently quantifying over all compact Hausdorff spaces, which do not form a set.) | |
| Oct 15, 2011 at 1:53 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 3.0 |
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| Oct 15, 2011 at 1:47 | comment | added | Mariano Suárez-Álvarez | (One can try to mod out $X$ by the relation "$x$ and $y$ cannot be separeted by disjoint open sets" —or its transtive closure, really— but the result is not Hausdorff; you can iterate this transfinitely, though, and you do get the space largest quotient. This is much more complicated/annoying/long to carry out) | |
| Oct 15, 2011 at 1:40 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 3.0 |