Automatic continuity of homomorphisms and fixed points on metric compacta

Christian Rosendal, Sławomir Solecki

Research output: Contribution to journalArticle

Abstract

We prove that arbitrary homomorphisms from one of the groups Homeo(2 ), Homeo(2)ℕ , Aut (ℚ, <), Homeo(ℝ}) or Homeo(S1) 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 of V. G. Pestov, that any action of the discrete group Homeo+(ℝ) by homeomorphisms on a compact metric space has a fixed point.

Original languageEnglish (US)
Pages (from-to)349-371
Number of pages23
JournalIsrael Journal of Mathematics
Volume162
DOIs
StatePublished - Dec 1 2007

ASJC Scopus subject areas

  • Mathematics(all)

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