Skip to main content
Article thumbnail
Location of Repository

Properness, Cauchy-indivisibility and the Weil completion of a group of isometries

By A. Manoussos and P. Strantzalos


In this paper we introduce a new class of metric actions on separable (not necessarily connected) metric spaces called "Cauchy-indivisible" actions. This new class coincides with that of proper actions on locally compact metric spaces and, as examples show, it may be different in general. The concept of "Cauchy-indivisibility" follows a more general research direction proposal in which we investigate the impact of basic notions in substantial results, like the impact of local compactness and connectivity in the theory of proper transformation groups. In order to provide some basic theory for this new class of actions we embed a "Cauchy-indivisible" action of a group of isometries of a separable metric space in a proper action of a semigroup in the completion of the underlying space. We show that, in case this subgroup is a group, the original group has a "Weil completion" and vice versa. Finally, in order to establish further connections between "Cauchy-indivisible" actions on separable metric spaces and proper actions on locally compact metric spaces we investigate the relation between "Borel sections" for "Cauchy-indivisible" actions and "fundamental sets" for proper actions. Some open questions are added.Comment: 28 page

Topics: Mathematics - General Topology, Primary 37B05, 54H20, Secondary 54H15
Year: 2011
OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.