Timeline for Amenability of $S^{\infty}$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 23, 2018 at 7:28 | vote | accept | Ali Taghavi | ||
| Feb 22, 2018 at 18:59 | comment | added | user95282 | @AliTaghavi In the second question, you probably mean a subgroup of a _locally _compact amenable group. With its usual Polish topology, $G$ is amenable. | |
| Feb 22, 2018 at 16:26 | answer | added | Taras Banakh | timeline score: 5 | |
| Feb 22, 2018 at 14:57 | comment | added | Taras Banakh | I think that your two questions are equivalent: $S_\omega$ admits a non-discrete locally compact topology if and only if $S_\omega$ is isomorphic to a dense subgroup of non-discrete locally compact topological group. This can be shown using the fact that the topology of point-wise convergence is the smallest group topology on $S_\omega$. So, now I am thinking on the existence of a non-discrete locally compact group topology on $S_\omega$ and cannot find a quick answer (neither my collegues - Ravsky, Gutik -- that work in this field). This is an interestng question. | |
| Feb 22, 2018 at 14:46 | comment | added | Ali Taghavi | @TarasBanakh And the discrete one is not amenable. But is it isomorphic to a dense subgroup of an amenable group? | |
| Feb 22, 2018 at 14:03 | comment | added | Taras Banakh | I am afraid that the unique locally compact group topology on $S^\infty$ is the discrete topology. | |
| Feb 22, 2018 at 11:15 | history | asked | Ali Taghavi | CC BY-SA 3.0 |