Automatic continuity of homomorphisms and fixed points on metric compacta

Christian Rosendal, Slawomir Solecki

We prove that arbitrary homomorphisms from one of the groups ${\rm Homeo}(\ca)$, ${\rm Homeo}(\ca)^\N$, ${\rm Aut}(\Q,<)$, $\mathrm{Homeo}(\mathbb{R})$, or $\mathrm{Homeo}(S^1)$ into a separable…