Timeline for A fixed point problem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2013 at 16:09 | vote | accept | dimo | ||
| Jul 29, 2013 at 1:43 | comment | added | Pietro Majer | (sorry, "exchange" is not the right word. What I mean is: in the former case we have $V < f(V)$ and $W > f(W)$ in the order of $S_r$) | |
| Jul 28, 2013 at 23:17 | history | edited | Pietro Majer | CC BY-SA 3.0 |
deleted 163 characters in body
|
| Jul 28, 2013 at 22:11 | comment | added | Pietro Majer | Either it does or not: if it does not, then it exchanges two points, and in this case you do not need $f(S_r)\subset S_r$ to conclude. | |
| Jul 28, 2013 at 21:17 | comment | added | Pietro Majer | To prove the last statement, we may consider another alternative: either $S_r$ is mapped into itself, so $f_{|S_r}$ has a fixed point there, or not, in which case some point $W\in S_r$ is mapped to $V$ by connection (this because $A\setminus\{V\}$ is disconnected): but then $f$ exchanges $V$ and $W$ and has a fixed point in between. | |
| Jul 28, 2013 at 21:01 | history | answered | Pietro Majer | CC BY-SA 3.0 |