Timeline for A family of subsets with a "gluing" property
Current License: CC BY-SA 2.5
4 events
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| Jul 6, 2010 at 22:13 | comment | added | joshuahhh | Yep. You are thinking about this on much the same lines as I did. And you're entirely right that the recursive decomposition fails to work, at least in any obvious way. Thanks for your thoughts, though! | |
| Jun 17, 2010 at 16:48 | comment | added | Victor Protsak | You are right, Joel, and it occurred to me as well (offline). What is worse, this will necessarily be the case for each $X_i$ at the first level. Unfortunately, the maximal proper connected subsets are not going to form a partition. I am no longer convinced that there is clean answer. | |
| Jun 17, 2010 at 12:45 | comment | added | Joel David Hamkins | Since the whole set $S$ can be added to any family $F$ and still form a connected family, your top-level partition might just be $S$ itself. For the induction step in your analysis, therefore, you should look at "maximal proper" connected subsets. | |
| Jun 17, 2010 at 4:14 | history | answered | Victor Protsak | CC BY-SA 2.5 |