On the Chabauty space of locally compact abelian groups

Cornulier, Yves

doi:10.2140/agt.2011.11.2007

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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

Volume 11, issue 4 (2011)