Timeline for Simple closed curves in a simply connected domain
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2023 at 11:52 | comment | added | Pietro Majer | (for instance $X_k:=\{x: 1/k\le \|x\|\le 1-1/k\}$ is increasing and converges to $\overline B_1$ but $\partial X_k$ does not converge to $\partial B_1$) | |
| Dec 7, 2023 at 17:31 | comment | added | user111 | Sure, I agree ! | |
| Dec 7, 2023 at 14:36 | comment | added | Pietro Majer | But the last implication is not immediate, although it's based on standard facts. Since it is the point of the question it seems safer to give a complete proof. | |
| Dec 7, 2023 at 10:02 | comment | added | user111 | With the notations of the given answer, the sequence of sets $h(\overline B_r)$ gives an exhaustion of $U$ by compact sets, and it is known that the Hausdorff distance behaves well under increasing sequence of nonempty compact sets, namely $d_H(h(\overline B_r),\overline U)\to0$ as $r\to1$. In particular $d_H(\Gamma_r,\partial U)\to0$. | |
| Dec 7, 2023 at 2:53 | vote | accept | D.S. Lipham | ||
| Dec 6, 2023 at 23:22 | answer | added | Pietro Majer | timeline score: 2 | |
| Dec 6, 2023 at 17:10 | history | asked | D.S. Lipham | CC BY-SA 4.0 |