Timeline for another question about connected open sets in $R^2$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 27, 2014 at 17:41 | answer | added | Anton Petrunin | timeline score: 2 | |
| Nov 27, 2014 at 16:55 | answer | added | Alexandre Eremenko | timeline score: 5 | |
| Nov 27, 2014 at 16:46 | history | edited | user173856 | CC BY-SA 3.0 |
[Edit removed during grace period]
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| Nov 27, 2014 at 16:21 | comment | added | Mirko | You know better than me what your question is, yet, the way I think of it is different: Does there exist $x$ in the boundary of $U$ such that for every $r>0$ the ball $B(x,r)$ intersects $U$ in a connected set? The answer to your question would be trivially yes if $U$ is bounded (just take a large enough ball containing $U$), but on the other hand it doesn't feel like boundedness should have anything to do with this question. Or, you may ask if there are $x\in Bd(U)$ such that for every $\epsilon$ there is $\delta$ with $U\cap B(x,\delta)$ connected. I don't know but might be edited some way. | |
| Nov 27, 2014 at 16:02 | comment | added | user173856 | I do not think S. Carnahan's answer can solve my question! | |
| Nov 27, 2014 at 15:56 | comment | added | Mirko | The answer provided by @S. Carnahan to your original question seems to come close to answering the present modified version. At least it seems you need that $U$ is fractal (or has fractal boundary). | |
| Nov 27, 2014 at 15:42 | history | asked | user173856 | CC BY-SA 3.0 |