Timeline for On the definition of locally compact for non-Hausdorff spaces
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2017 at 20:23 | vote | accept | Phil-W | ||
| Feb 25, 2017 at 12:28 | answer | added | Arno | timeline score: 2 | |
| Feb 25, 2017 at 11:11 | comment | added | abx | @Phil-W: compare with the 3 possible definitions given by the english Wikipedia page, which concludes by "In almost all applications, locally compact spaces are indeed also Hausdorff". | |
| Feb 25, 2017 at 11:03 | comment | added | Johannes Hahn | The reason why LC2 and LCn2 are the "right" definitions is because they actually capture what "locally X" means. We don't care about "a" neighbourhood. Things hold locally if they hold on arbitrary small neighbourhoods. That LC1 is equivalent to LC2 in Hausdorff spaces is simply an "accident" that is rooted in the non-obvious interplay between compactness, separation axioms ($T_2+compact\implies T_3$) and a similarly accidental side effect of $T_3$ being equivalent to "locally closed". | |
| Feb 25, 2017 at 10:41 | comment | added | Phil-W | @abx : what are those good reasons ? | |
| Feb 25, 2017 at 10:14 | comment | added | abx | You are probably aware that in most french books (following Bourbaki, and including Wikipedia), a locally compact space is Hausdorff by definition -- with good reasons in my view. | |
| Feb 25, 2017 at 7:26 | comment | added | Nate Eldredge | LCn1 seems clearly "wrong" since it is satisfied by every connected space, even those such as comb space or the topologist's sine curve which violate the whole idea of local connectedness. | |
| Feb 25, 2017 at 4:14 | answer | added | Todd Trimble | timeline score: 16 | |
| Feb 25, 2017 at 3:44 | history | asked | Phil-W | CC BY-SA 3.0 |