Automatic continuity of homomorphisms and fixed points on metric compacta
| dc.creator | Rosendal, Christian | |
| dc.creator | Solecki, Slawomir | |
| dc.date | 2006-04-26 | |
| dc.date.accessioned | 2026-07-07T07:11:18Z | |
| dc.date.available | 2026-07-07T07:11:18Z | |
| dc.description | We prove that arbitrary homomorphisms from one of the groups ${\rm Homeo}(\ca)$, ${\rm Homeo}(\ca)^\N$, ${\rm Aut}(\Q,<)$, ${\rm Homeo}(\R)$, or ${\rm Homeo}(S^1)$ into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result on V.G. Pestov, that any action of the discrete group ${\rm Homeo}_+(\R)$ by homeomorphisms on a compact metric space has a fixed point. | |
| dc.identifier | https://arxiv.org/abs/math/0604575 | |
| dc.identifier | http://arxiv.org/abs/math/0604575 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111707 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.title | Automatic continuity of homomorphisms and fixed points on metric compacta | |
| dc.type | text |