Timeline for Self-homeomorphism of Stone-Čech boundary with an isolated fixed point
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2021 at 11:17 | comment | added | KP Hart | See below: a fixed point of an autohomeomorphism of $\omega^*$ is necessarily a P-point. | |
| May 3, 2021 at 13:24 | vote | accept | YCor | ||
| May 3, 2021 at 13:20 | comment | added | YCor | Great! Of course if you can achieve one fixed point you can achieve $n\ge 1$ fixed points (using that the space is homeomorphic to $n$ copies of itself). In this direction one could ask whether every closed subset is the fixed point set of a self-homeomorphism. In this direction and also involving periodicities one could then ask if for every family $(K_n)_{n\ge 1}$ of closed subsets, satisfying $K_m\subset K_n$ whenever $n$ divides $n$, there exists a self-homeo $f$ for which $\mathrm{Fix}(f^n)=K_n$ for every $n$ (unless I'm missing an obvious obstruction). | |
| May 3, 2021 at 13:18 | history | edited | Will Brian | CC BY-SA 4.0 |
deleted 3 characters in body
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| May 3, 2021 at 13:06 | history | answered | Will Brian | CC BY-SA 4.0 |