Timeline for Can you write $\mathbb R^2$ as a disjoint union of two totally disconnected sets?
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2, 2015 at 11:21 | comment | added | Włodzimierz Holsztyński | Every $n$-dimensional separable metric space is a union of $\ n+1\ $ subspaces of dimension zero, but not of less than $\ n+1$. | |
| Mar 2, 2015 at 11:15 | comment | added | Włodzimierz Holsztyński | @EricWofsey -- yes, into 3 sets of dimension $0$ (better than just totally disconnected), it's quite pleasing: $\ \mathbb R_{k\,\ 2-k}\ $ is the set of all points which have exactly $\ k\ $ coordinates rational, and $\ 2-k\ $ irrational $\ (\ k=0\ 1\ 2).\ $ Now you can decompose $\ \mathbb R^n\ $ into $\ n+1\ $ zero-dimensional sets for each natural $\ n.$ | |
| Feb 28, 2015 at 5:07 | answer | added | George Lowther | timeline score: 13 | |
| Feb 27, 2015 at 12:35 | answer | added | Włodzimierz Holsztyński | timeline score: 2 | |
| Feb 26, 2015 at 22:37 | comment | added | Eric Wofsey | According to the comments on Gerald Edgar's answer, it is possible to write $\mathbb{R}^2$ as a union of three totally disconnected sets. Is there an easy way to construct such sets? | |
| Feb 26, 2015 at 16:27 | comment | added | Włodzimierz Holsztyński | @ToddTrimble -- thank you for reopening the question. The respective theorem in the previous thread (with path in the title) stated there by Gerald Edgar had in Gerald's proof an error which made that attempt at a proof virtually empty. | |
| Feb 26, 2015 at 3:24 | answer | added | Włodzimierz Holsztyński | timeline score: 13 | |
| Feb 25, 2015 at 19:57 | answer | added | Kristal Cantwell | timeline score: 7 | |
| Feb 25, 2015 at 19:57 | history | edited | Christian Remling | CC BY-SA 3.0 |
added 10 characters in body; edited title
|
| Feb 25, 2015 at 19:36 | history | reopened |
Benjamin Steinberg Joonas Ilmavirta Jeremy Rickard Emil Jeřábek Bjørn Kjos-Hanssen |
||
| Feb 25, 2015 at 18:53 | review | Reopen votes | |||
| Feb 25, 2015 at 19:39 | |||||
| Feb 25, 2015 at 17:30 | comment | added | Todd Trimble | Meta: meta.mathoverflow.net/a/2154/2926 | |
| Feb 25, 2015 at 16:36 | comment | added | Włodzimierz Holsztyński | Nima, it wouldn't really hurt to add the definition of the totally disconnected space (or set). There are many related notions. You could at least point to a reference--just to show that you yourself understand this notion in the way others do. Someone may roughly know the topic without narrowly working exactly on notions like totally disconnected, extremally disconnected, zero-dimensional according to this or other definition, etc. | |
| Feb 25, 2015 at 15:47 | history | closed |
YCor Alex Degtyarev Stefan Kohl♦ Karl Schwede Dirk |
Duplicate of Can you explicitly write $\mathbb{R}^2$ as a disjoint union of two totally path disconnected sets? | |
| Feb 25, 2015 at 14:15 | comment | added | Todd Trimble | Although (regarding my prior comment) @Włodzimierz commented below Gerald's answer, raising a possible objection, to which there hasn't been a response. Not wishing to put him on the spot, I hope Włodzimierz (or Gerald or someone else) has some spare time to answer this. | |
| Feb 25, 2015 at 13:51 | review | Close votes | |||
| Feb 25, 2015 at 15:47 | |||||
| Feb 25, 2015 at 12:05 | comment | added | Todd Trimble | Gerald Edgar answered this here: mathoverflow.net/a/44320/2926 | |
| Feb 25, 2015 at 11:39 | comment | added | Włodzimierz Holsztyński | It is not possible. Where does this problem come from? | |
| Feb 25, 2015 at 11:36 | review | Low quality posts | |||
| Feb 25, 2015 at 11:37 | |||||
| Feb 25, 2015 at 11:21 | review | First posts | |||
| Feb 25, 2015 at 11:27 | |||||
| Feb 25, 2015 at 11:19 | history | asked | Nima | CC BY-SA 3.0 |