Timeline for infinite dimensional polyhedra
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2014 at 13:11 | vote | accept | Ankur | ||
| Feb 7, 2014 at 14:46 | answer | added | Gerald Edgar | timeline score: 5 | |
| Feb 7, 2014 at 11:59 | comment | added | Manfred Weis | In the case of an countably infinite number of half-spaces, it should also be mentioned whether the set of normal directions is discrete or dense on the unit sphere. | |
| Feb 7, 2014 at 10:07 | comment | added | Manfred Weis | @Ankur: I miss the restriction to a countable infinite number of intersecting half-spaces in the problem description; otherwise a sphere would also be an infinite convex polyhedron. Maybe in the title the restriction to convex polyhedra should also be mentioned. | |
| Feb 7, 2014 at 9:01 | answer | added | alpha | timeline score: 3 | |
| Feb 7, 2014 at 3:08 | answer | added | Tom LaGatta | timeline score: 0 | |
| Feb 7, 2014 at 2:59 | comment | added | Ankur | In my case, I could have infinitely many half-spaces intersecting. Can something be said about this case? (I edited my question with this clarification) | |
| Feb 7, 2014 at 2:58 | history | edited | Ankur | CC BY-SA 3.0 |
added 77 characters in body
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| Feb 6, 2014 at 20:35 | comment | added | Wlodek Kuperberg | @LevBorisov: The map you describe is in fact a projecion onto a finite-dimensional space in a direction parallel to each of the defining half-spaces. Therefore the original, infinite-dimensional polytope is the Cartesian product of a finite-dimensional one with an infinite-dimensional space. You should write your comment in the "answer" box. | |
| Feb 6, 2014 at 19:42 | review | First posts | |||
| Feb 6, 2014 at 19:48 | |||||
| Feb 6, 2014 at 19:42 | comment | added | Joseph O'Rourke | You might look at Paolo d'Alessandro, "Generalizing polyhedra to infinite dimension," 2011. PDF download link. | |
| Feb 6, 2014 at 19:41 | comment | added | Lev Borisov | If you have a finite number of half-spaces, then presumably you have a finite number of linear functions. Then you want to consider the span of these linear functions. This would give you a map from your infinite-dimensional space to a finite-dimensional space and all of the polytope business comes from the latter. So I think that you can separate the infinite-dimensional issues and the polyhedral issues. | |
| Feb 6, 2014 at 19:24 | history | asked | Ankur | CC BY-SA 3.0 |