度量空间上同态与不动点的自动连续性
Automatic continuity of homomorphisms and fixed points on metric compacta
摘要：
证明了从群${\rm Homeo}(\ca)$，${\rm Homeo}(\ca)^\N$，${\rm Aut}(\Q,<)$，${\rm Homeo}(\R)$，或${\rm Homeo}(S^1)$到可分群的任意同态都是自动连续的.这对将这些群体表示为离散群体产生了影响。例如，下面结合V.G. Pestov证明了离散群${\rm Homeo}_+(\R)$在紧度量空间上的同胚作用有不动点。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
