Timeline for Can you explicitly write $\mathbb{R}^2$ as a disjoint union of two totally path disconnected sets?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2023 at 7:09 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Nov 6, 2015 at 12:56 | history | edited | Ramiro de la Vega | CC BY-SA 3.0 |
added 11 characters in body; edited title
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| Feb 24, 2013 at 21:01 | answer | added | Włodzimierz Holsztyński | timeline score: 1 | |
| Oct 31, 2010 at 15:59 | comment | added | Andrés E. Caicedo | Mariano: No, you are assuming CH there. It means "biject with the first ordinal in bijection with the reals." | |
| Oct 31, 2010 at 13:28 | answer | added | Gerald Edgar | timeline score: 9 | |
| Oct 31, 2010 at 12:13 | answer | added | Patrick Tam | timeline score: 0 | |
| Nov 18, 2009 at 6:52 | comment | added | Mariano Suárez-Álvarez | What does "well-order with order-type the continuum"? Maybe "biject the set of paths with the first uncountable ordinal" so that all initial segments of the ordinal are numerable? | |
| Oct 9, 2009 at 23:10 | answer | added | George Lowther | timeline score: 62 | |
| Oct 9, 2009 at 20:17 | comment | added | Anton Geraschenko | @Eric: that's awesome! What else could you possibly do? | |
| Oct 9, 2009 at 2:32 | comment | added | Eric Wofsey | Here's a nonexplicit construction. Enumerate (well-order) all possible paths with order-type the continuum. By induction, put one point from each path in each of the sets of the partition. This is possible since each path contains continuum many points and at any stage of the induction, you've only chosen where less than continuum points go. | |
| Oct 6, 2009 at 23:57 | comment | added | Anton Geraschenko | I'd be happy with a non-explicit way to make such a partition. | |
| Oct 6, 2009 at 22:06 | history | asked | 20 questions | CC BY-SA 2.5 |