Timeline for Continuous maps which send intervals of $\mathbb{R}$ to convex subsets of $\mathbb{R}^2$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2015 at 23:56 | answer | added | Michael Hardy | timeline score: 3 | |
| Sep 4, 2015 at 21:28 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
TeX fix
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| Mar 25, 2015 at 16:22 | comment | added | Abcd | Thank you, Jairo, that was exactly what I was looking for ! Your comment should be an answer, by the way. | |
| Mar 24, 2015 at 19:48 | comment | added | Jairo Bochi | This is the Mihalik-Wieczorek problem. It's indeed devilish. :) Let me remark that if you only ask for the convexity of $f(I)$ for the intervals of the form $I=[0,t]$ then it is possible to construct a space-filling curve: see arxiv.org/abs/1407.5204 and the references there. | |
| Mar 20, 2015 at 18:03 | answer | added | Igor Rivin | timeline score: 0 | |
| Mar 20, 2015 at 15:48 | comment | added | Abcd | Yes, I tried. If one aims to construct a counterexample, then one can discretized the whole situation, and try to draw a path on a $n \times n$ grid such that 1) the path fills the square and 2) satisfies the convexity condition in an appropriate approximate sense. The problem is that in order to be able to extract a limit, one has to ensure the equicontinuity of our family of paths. I've never succeeded in drawing an equicontinuous family of paths satisfying 1) and 2) above (but of course it doesn't mean that it is not possible). | |
| Mar 20, 2015 at 15:09 | comment | added | Francesco Polizzi | I'm far for being an expert so I'm not sure whether this makes sense, anyway did you try to build a counterexample by using some kind of plane-filling curve? | |
| Mar 20, 2015 at 14:52 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
added top-level tags
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| Mar 20, 2015 at 14:20 | review | First posts | |||
| Mar 20, 2015 at 14:36 | |||||
| Mar 20, 2015 at 14:16 | history | asked | Abcd | CC BY-SA 3.0 |