Timeline for Topology of length spaces
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19, 2019 at 4:10 | vote | accept | Tim Campion | ||
| Jun 19, 2019 at 4:10 | comment | added | Tim Campion | Fantastic, thanks! | |
| Jun 19, 2019 at 4:07 | comment | added | Sergio Zamora | My bad, wrong reference projecteuclid.org/euclid.bams/1183514375 Theorem 8 | |
| Jun 15, 2019 at 15:56 | comment | added | Tim Campion | Upon closer inspection, Bing only shows that a compact, locally connected continuum has a convex metric if additionally it is finite-dimensional. I'd be curious if the finite-dimensionality hypothesis can be lifted. | |
| Jun 15, 2019 at 1:03 | vote | accept | Tim Campion | ||
| Jun 15, 2019 at 15:59 | |||||
| Jun 15, 2019 at 1:02 | comment | added | Tim Campion | Thanks, I see that is indeed almost immediate! | |
| Jun 15, 2019 at 1:00 | comment | added | Sergio Zamora | They are: Take $p$ in a length space and an (open) ball $B$ of radius $r$ around $p$. Pick $q \in B$, then $d(p,q) < r$ and there is a curve of length less than $r$ joining $p$ and $q$. By the triangle inequality, this curve lies entirely in $B$, so $B$ is path connected. | |
| Jun 15, 2019 at 0:26 | comment | added | Tim Campion | Thanks! That Bing reference is just what I was hoping for! I'm a bit confused, though -- are you saying that length spaces are locally path connected? Or are you saying rather that it must be taken as an additional assumption? I still can't see why length spaces should be locally path connected, so if that's the claim, could you give a hint? | |
| Jun 15, 2019 at 0:16 | history | answered | Sergio Zamora | CC BY-SA 4.0 |