Timeline for Compactness of the class of connected sets with perimetre smaller than 1?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2011 at 8:21 | vote | accept | kaleidoscop | ||
| Aug 4, 2011 at 8:44 | answer | added | Sergei Ivanov | timeline score: 12 | |
| Aug 3, 2011 at 19:06 | comment | added | Theo Johnson-Freyd | Hi Remark: I don't know the answer to your question, but here's a potential strategy. As Tom Leinster has been explaining for some time now (see eg his posts on n-Category Cafe), another good definition of perimeter of a closed set $X$ is $\frac{\partial}{\partial\epsilon} \bigr|_{\epsilon=0} \mathrm{Vol}(X_\epsilon)$, where $X_\epsilon$ is the set of all points within distance ϵ of X. Perhaps this is the same as your definition. Anyway, then perhaps you can successfully swap a limit somewhere when computing a limit in Hausdorff topology. | |
| Aug 3, 2011 at 16:08 | history | asked | kaleidoscop | CC BY-SA 3.0 |