Timeline for Extend Homeomorphism to Uniformly Continuous Function
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2013 at 16:56 | comment | added | David Collins | Nope, I think I'm missing the point. It's not that it gets close together, it's that some part of it is infinitely long. | |
| Jun 25, 2013 at 15:58 | comment | added | David Collins | No, I don't think that's quite right. I think I mean there exists $\epsilon>0$ such that for every $\delta$ with $0<\delta<\epsilon$ and for every $x\in A$, the intersection of $A$ with the $\delta$ ball around $x$ is connected. | |
| Jun 24, 2013 at 21:59 | comment | added | David Collins | Hmm, that's a nice counterexample. What if we include a uniform bound on being connected locally, something like: there exists $\epsilon>0$ such that for all $x\in A$, the intersection of $A$ and the $\epsilon$-ball around $x$ is connected. It seems like that condition might even imply the finite volume. | |
| Jun 22, 2013 at 6:50 | history | answered | Nik Weaver | CC BY-SA 3.0 |