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On the Chabauty space of locally compact abelian groups

Yves Cornulier
Algebraic & Geometric Topology 11 (2011) 2007–2035
DOI: 10.2140/agt.2011.11.2007
Abstract

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.

Keywords
Chabauty topology, locally compact abelian groups
Mathematical Subject Classification 2000
Primary: 22B05
Secondary: 20E15, 43A25, 54D05, 54F45
References
Publication
Received: 6 December 2010
Revised: 8 April 2011
Accepted: 9 April 2011
Published: 20 July 2011
Authors
Yves Cornulier
Laboratoire de Mathématiques
Bâtiment 425
Université Paris-Sud 11
91405 Orsay
France