Timeline for Explicit extension of Lipschitz function (Kirszbraun theorem)
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2020 at 17:09 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question has been bumped anyway)
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| Jan 26, 2020 at 18:17 | history | edited | Pietro Majer | CC BY-SA 4.0 |
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| Jan 26, 2020 at 10:07 | answer | added | Pietro Majer | timeline score: 4 | |
| Jan 25, 2020 at 20:01 | answer | added | Aryeh Kontorovich | timeline score: 2 | |
| Jan 25, 2020 at 16:24 | answer | added | jlewk | timeline score: 6 | |
| May 11, 2012 at 10:52 | vote | accept | gondolier | ||
| May 11, 2012 at 10:52 | vote | accept | gondolier | ||
| May 11, 2012 at 10:52 | |||||
| May 10, 2011 at 23:06 | comment | added | Anton Petrunin | If the dimension is finite, there is no need to use Hausdorff's maximal principle. Choose a dense countable set in U and extend the map to set of all rational points. The obtained map can be extended to a Lipschitz one on whole space. | |
| May 10, 2011 at 18:31 | comment | added | Bill Johnson | If the space is separable, you can choose a countable dense set of the complement of the domain of the function and recursively define the extension to include that countable dense set and then extend to the whole space by continuity. The entire proof is then explicit once you have the countable dense set and an ordering on it. | |
| May 10, 2011 at 18:29 | comment | added | Bill Johnson | The key step in the proof of Kirszbraun's theorem involves extending the function to one more point. You write down the conditions on an extension which make the extension have the same Lipschitz constant and show that it is possible to satisfy the conditions. It is easy to make the extension explicit. TBC | |
| May 10, 2011 at 17:30 | answer | added | Sergei Ivanov | timeline score: 10 | |
| May 10, 2011 at 16:11 | comment | added | Theo Buehler | Offhand I don't know how constructive this is, but are you aware of the paper of Lang-Pavlovic-Schroeder's springerlink.com/content/5pd0u4yr5frrvbyk ? | |
| May 10, 2011 at 15:49 | history | asked | gondolier | CC BY-SA 3.0 |