Timeline for Meeting a set of lines in a generalization of $\mathbb{R}^n$
Current License: CC BY-SA 3.0
5 events
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| Sep 19, 2017 at 16:25 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 8 characters in body
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| Aug 31, 2017 at 8:30 | comment | added | Péter Komjáth | This is the dual of your earlier question: if ${\cal H}$ is a set of (nonempty) subsets of $S$, then for $x\in S$ define ${\cal H}_x=\{H\in{\cal H}:x\in H\}$. Notice that if $H\cap H'|\leq 1$ for $H\neq H'\in{\cal H}$, then $|{\cal H}_x\cap {\cal H}_y|\leq 1$ for $x\neq y$, and a minimal covering set (in one sens) of ${\cal H}$ is a minimal covering set (in the other sense) of the other. I have some thoughts on this, will send you an email. | |
| Aug 31, 2017 at 8:28 | comment | added | Dominic van der Zypen | @YBerman Thanks for your comment & example. In your example, the set $M=\{0\}$ has the desired properties. The question is whether for all infinite sets $S$ and collections ${\cal L}$ of subsets meeting the desired properties, such a set $M$ exists. | |
| Aug 31, 2017 at 7:25 | comment | added | yberman | What if $S$ is the non-negative integers, $\mathcal{L} = \{\ \{0, n\}: n > 0\ \}$, and $M = \{0\}$. I suspect I don't fully understand the question. | |
| Aug 31, 2017 at 7:16 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |