Timeline for Dehn and the Jordan curve theorem
Current License: CC BY-SA 4.0
10 events
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| May 25, 2023 at 11:47 | history | edited | coudy | CC BY-SA 4.0 |
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| Aug 30, 2022 at 9:10 | history | edited | Sam Nead |
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| Aug 30, 2022 at 7:48 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Aug 30, 2022 at 1:28 | history | edited | Sam Nead |
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| Aug 18, 2020 at 18:36 | comment | added | Timothy Chow | But Hales addresses this in Section 4.2. Jordan never claims that the segments of a polygon cannot intersect. He (initially) allows the segments of the polygon to intersect, and page 93 of his proof describes a finite process of removing small loops from the polygon to make it simple. | |
| Aug 18, 2020 at 18:33 | comment | added | Timothy Chow | At the time Hales wrote his paper, he was unaware of Guggenheimer's paper. I asked Hales about this. He said Guggenheimer had two objections. The first was that Jordan didn't prove the theorem for polygons. Hales discusses this point in his paper. The second objection (p 194) was, "What is missing is a proof that for a Jordan curve $x(t)$, $0\le t \le 1$, and $\delta>0$ there is an $\epsilon_0$ such that the segments $x(t_i) x(t_{i+1}), x(t_j) x(t_{j+1})$ of a polygon of vertices $x(t_0),\ldots,x(t_N)$ cannot intersect if $t_{k+1}-t_k<\epsilon\le\epsilon_0$ and $|x(t_{j+1})-x(t_i)| <\delta$." | |
| Oct 23, 2019 at 20:23 | comment | added | Timothy Chow | Not directly relevant, but Hales has championed the view that Jordan's original proof was correct. mizar.org/trybulec65/4.pdf | |
| Oct 23, 2019 at 15:49 | comment | added | John Stillwell | To clarify, Dehn's proof is for the polygonal Jordan curve theorem. He was interested in deriving it from a small subset of Hilbert's axioms for geometry. | |
| Oct 23, 2019 at 11:47 | comment | added | Sam Nead | The Briscoe center is at UT Austin. Try contacting a mathematician who works there; eg Cameron Gordon? | |
| Oct 23, 2019 at 10:43 | history | asked | coudy | CC BY-SA 4.0 |