Timeline for Generalizing the Mazur-Ulam theorem to convex sets with empty interior in Banach spaces
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2016 at 0:10 | vote | accept | Mikhail Ostrovskii | ||
| May 2, 2016 at 19:05 | comment | added | Uri Bader | That's a beautiful, Gideon. Next challenge: a fixed point free example :) Uri. | |
| May 2, 2016 at 15:49 | comment | added | Bill Johnson | Nice example. As for the edit, I just could not resist. :) | |
| May 2, 2016 at 15:48 | history | edited | Bill Johnson | CC BY-SA 3.0 |
Corrected grammar.
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| May 2, 2016 at 15:11 | comment | added | BS. | Beautiful (counter)-examples ! | |
| May 2, 2016 at 14:33 | comment | added | Gideon Schechtman | Consider the subset of $M_1$ consisting of the (non decreasing) functions which take constant values in $\{0,1/n,2/n,\dots,1\}$ on each interval $((i-1)/n,i/n)$. There is a finite number of such functions and each function in $K$ and thus in $M_1$ is of distance at most $2/n$ from one of these functions. To prove the last claim note that each function in $K$ intersects at most $2/n$ of the $n^2$ $1/n\times 1/n$ squares of the natural $1/n$ grid. (I'm not very precise about the constant 2 above...) | |
| May 2, 2016 at 13:58 | comment | added | Nate Eldredge | I am having trouble seeing why $M_1, M_2$ are compact. Can you elaborate? | |
| May 2, 2016 at 13:48 | history | answered | Gideon Schechtman | CC BY-SA 3.0 |