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Lacunary free actions on the real line

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
20
Issue
2
Identifiers
DOI: 10.1016/0166-8641(85)90073-2
Keywords
  • 54H15
  • 57S25
  • 06A05
Disciplines
  • Biology
  • Mathematics
  • Medicine

Abstract

Abstract All groups of free homeomorphisms of the real line are determined up to topological conjugacy. Surprisingly, many of them are lacunary in the sense that no orbit is dense, although the groups themselves (with the exception of the infinite cyclic group) are dense subgroups of R +. Such pathological behaviour is, however, impossible for normal subgroups of transitive groups.

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