Automatic continuity of homomorphisms and fixed points on metric compacta TeX Export

@misc{citeulike:911150, abstract = {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.}, archivePrefix = {arXiv}, author = {Rosendal, Christian and Solecki, Slawomir}, citeulike-article-id = {911150}, citeulike-linkout-0 = {http://arxiv.org/abs/math.LO/0604575}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.LO/0604575}, eprint = {math.LO/0604575}, keywords = {descriptive-set-theory}, month = {Apr}, posted-at = {2006-10-24 14:23:35}, priority = {2}, title = {Automatic continuity of homomorphisms and fixed points on metric compacta}, url = {http://arxiv.org/abs/math.LO/0604575}, year = {2006} }

TY - ELEC ID - citeulike:911150 L3 - citeulike-article-id:911150 N2 - 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. TI - Automatic continuity of homomorphisms and fixed points on metric compacta KW - descriptive-set-theory AU - Rosendal, Christian AU - Solecki, Slawomir PY - 2006/Apr/26/ UR - http://arxiv.org/abs/math.LO/0604575 ER -