Timeline for Three modifications of connectedness
Current License: CC BY-SA 2.5
25 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2011 at 1:54 | answer | added | dan232 | timeline score: 0 | |
| Jul 15, 2010 at 16:34 | history | edited | porton | CC BY-SA 2.5 |
"binary relations; Post Made Community Wiki
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| Jul 15, 2010 at 16:07 | history | edited | porton | CC BY-SA 2.5 |
Clarified that a connector may be not extendable
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| Jul 15, 2010 at 3:54 | answer | added | Noah Stein | timeline score: 3 | |
| Jul 14, 2010 at 22:46 | history | edited | porton | CC BY-SA 2.5 |
Added informal explanation and examples
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| Jul 14, 2010 at 22:34 | comment | added | porton | Oh, in my last comment I messed r and not-r (negation of r) when telling about connectedness regarding topological space. | |
| Jul 14, 2010 at 22:24 | comment | added | porton | @Dan: The relation r of two sets A and B represents that A and B are in some sense "near" or "touch". For example r may be a proximity. As an other important example ArB may mean that the topological closure (given some topological space) of the set A in the subspace generated by the set $A\cup B$ does not intersect B neither the closure of B does intersect A. This is equivalent to the classic definition of connectedness of a set on topological space, because it happens if and only if A and B are open-closed on $A\cup B$. Should I add this to the question, or having here in comment is enough? | |
| Jul 14, 2010 at 22:17 | comment | added | porton | @Dan: Yes, they are elements of PA. I corrected the error in the question. | |
| Jul 14, 2010 at 22:16 | history | edited | porton | CC BY-SA 2.5 |
Error: X, Y \in A -> X, Y \in \mathcal{P} A
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| Jul 14, 2010 at 22:04 | comment | added | Dan Ramras | Also, it seems to me you could at least explain your conception of what the relation r represents, since many people will not care to click on the link in order to find out. | |
| Jul 14, 2010 at 22:03 | comment | added | Dan Ramras | @Porton: In the definition of CC(r), did you mean to say that X and Y are elements of PA, i.e. subsets of A? In the question, you wrote that they're elements of A. (Your draft article seems to agree with what I'm suggesting, though.) | |
| Jul 14, 2010 at 21:32 | comment | added | Yemon Choi | @Harry: on this occasion I'd prefer us to play the ball, and not the man | |
| Jul 14, 2010 at 21:31 | comment | added | Yemon Choi | @Noah: I think that the question could be left up a bit longer until someone comes along with a more specialized viewpoint or priorexperience of wh this kind of stuff does/doesn't work. (Should I make this a vote not to close, as it were, or have I misunderstood the new system?) | |
| Jul 14, 2010 at 21:31 | comment | added | Harry Gindi | mathematics21.org/abel-prize.html | |
| Jul 14, 2010 at 21:12 | history | edited | porton | CC BY-SA 2.5 |
$U$ -> $\mathcal{P}U$
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| Jul 14, 2010 at 20:38 | comment | added | porton | @Noah: I wonder, do you consider my above mentioned article too specific?! In fact it is very general. Or to be too specific and very general are compatible accordingly you opinion? If the article is not too specific, then the question is also not too specific. It seems that you've not looked into my article before voting. Bad. | |
| Jul 14, 2010 at 20:22 | comment | added | Noah Snyder | I voted to close as "too localized." It really seems way too specific with very little motivation. | |
| Jul 14, 2010 at 19:55 | comment | added | David Steinberg | @Martin: I saw the link, but I maintain that including motivation and relationship to familiar ideas might increase the number of responses. @Porton: I am not a topologist, so perhaps it is not surprising that your motivation is unclear to me | |
| Jul 14, 2010 at 19:24 | comment | added | porton | @David: I added a reference to the article, where the problem arises, above the question. Is the idea understandable from my too rough draft? | |
| Jul 14, 2010 at 19:23 | history | edited | porton | CC BY-SA 2.5 |
Added ref to the article above the question
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| Jul 14, 2010 at 19:13 | history | edited | porton | CC BY-SA 2.5 |
Corrected: binary relation on U -> binary relation on PU
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| Jul 14, 2010 at 19:08 | comment | added | Martin Brandenburg | @David: I think this is answered in the linked article. | |
| Jul 14, 2010 at 19:05 | comment | added | David Steinberg | You might increase the number of responses by giving some motivation (why generalize connectedness?) or by comparing familiar ideas (how is it a generalization of connectedness?) | |
| Jul 14, 2010 at 18:47 | history | edited | porton | CC BY-SA 2.5 |
Ref to proof in one direction in my draft article.
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| Jul 14, 2010 at 18:29 | history | asked | porton | CC BY-SA 2.5 |