Timeline for Characterization of Tychonoff spaces in terms of open sets
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2016 at 21:09 | answer | added | Joseph Van Name | timeline score: 3 | |
| May 18, 2011 at 7:50 | answer | added | KP Hart | timeline score: 5 | |
| May 8, 2011 at 12:52 | comment | added | mathahada | There's a natural bijection between the set of continuous functions from a $T_0$ space to the Sierpinski space and the topology of the space, but there's no such bijection between the topology of a regular space and the the set of continuous functions to the unit interval. I don't know category theory so I don't know how to make this precise but I think you should get the intuitive feeling that the Sierpinski space is in some sense canonical and minimal. Anyway the answer given is what I've been looking for (I actually read the book but managed to miss that part) | |
| May 8, 2011 at 12:31 | vote | accept | mathahada | ||
| May 8, 2011 at 11:35 | comment | added | Qiaochu Yuan | I don't necessarily buy the distinction you're making between open sets and "external objects." After all, talking about open sets is the same thing as talking about functions to the Sierpinski space. Does the Sierpinski space count as an external object? | |
| May 8, 2011 at 11:17 | answer | added | Karol Szumiło | timeline score: 9 | |
| May 8, 2011 at 10:53 | comment | added | mathahada | I don't think, because it still makes a reference to an external object. | |
| May 8, 2011 at 10:31 | comment | added | Chris Eagle | Here's one $\mathbb{R}$-free characterization: a space is Tychonoff iff it has a Hausdorff compactification. Is that the sort of thing you want? | |
| May 8, 2011 at 10:29 | comment | added | Kevin Ventullo | en.wikipedia.org/wiki/Tychonoff_space#Embeddings | |
| May 8, 2011 at 8:58 | history | asked | mathahada | CC BY-SA 3.0 |