Timeline for Can we approximate any open set by sub-domains with smooth boundary?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2017 at 3:11 | vote | accept | Guomin Liu | ||
| Oct 22, 2017 at 23:34 | comment | added | Guomin Liu | @Bombyxmori I understand your idea， thanks！ | |
| Oct 22, 2017 at 23:34 | comment | added | Guomin Liu | @AntonPetrunin I understand your idea， thanks！ | |
| Oct 22, 2017 at 14:26 | answer | added | Mohammad Ghomi | timeline score: 10 | |
| Oct 22, 2017 at 7:58 | comment | added | Guomin Liu | @ Bombyx mori In fact, we can only have the function locally. You mean that we need to mollify the functions locally and then connect them? | |
| Oct 22, 2017 at 5:56 | comment | added | Bombyx mori | @GuominLiu: The critical value is a set of measure $0$. So you can avoid it by Sard's theorem. The regular value providing level sets which are dense subsets approximating $A$, which is what you wanted. Another technique you may try is to convolute the function describing the hypersurface with a mollifer. | |
| Oct 22, 2017 at 5:37 | answer | added | ebro | timeline score: 0 | |
| Oct 22, 2017 at 2:30 | comment | added | Guomin Liu | @ Anton Petrunin Does the critical sets is has 0 Lebesgue measure on $\partial Q_n$? | |
| Oct 22, 2017 at 2:25 | comment | added | Guomin Liu | @ Anton Petrunin How to treat the critical sets? | |
| Oct 22, 2017 at 1:47 | review | Close votes | |||
| Oct 23, 2017 at 9:07 | |||||
| Oct 22, 2017 at 1:29 | comment | added | Anton Petrunin | Consider the function $f=\mathrm{dist}_{\partial A}$; approximate it by a smooth function and take level set of its regular value (provided by Sard's theorem). | |
| Oct 22, 2017 at 1:11 | review | First posts | |||
| Oct 22, 2017 at 3:53 | |||||
| Oct 22, 2017 at 1:06 | history | asked | Guomin Liu | CC BY-SA 3.0 |