Timeline for Hausdorff distance restricted to linear subspaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2019 at 13:07 | comment | added | Pietro Majer | For compact convex sets, I think Nik Weaver's example is typical, that is for any such sequence $Q_n$ in an infinite dimensional $V$, there exists a subspace $L$ for which the intersection is not continuous. If the $Q_n$ are non-empty, closed, "equi-uniformly convex" sets (hence they are not compact, unless $V$ is finite dimensional), then I guess the continuity of intersection with $L$ is true; maybe also with any closed convex $L$. | |
| Jul 26, 2019 at 16:34 | comment | added | Nik Weaver | No problem, you're welcome. | |
| Jul 26, 2019 at 15:28 | comment | added | Steve | @NikWeaver That was simpler than expected, thanks! | |
| Jul 26, 2019 at 14:50 | comment | added | Nik Weaver | Let $Q$ be the line segment joining $(0,0)$ and $(1,0)$ and let $Q_n$ be the line segment joining $(0,1/n)$ and $(1,0)$. | |
| Jul 26, 2019 at 14:17 | comment | added | Nik Weaver | This already fails in $\mathbb{R}^2$. | |
| Jul 26, 2019 at 13:49 | history | asked | Steve | CC BY-SA 4.0 |