Algebraic & Geometric Topology

On the Chabauty space of locally compact abelian groups

Yves Cornulier

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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.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2007-2035.

Dates
Received: 6 December 2010
Revised: 8 April 2011
Accepted: 9 April 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715261

Digital Object Identifier
doi:10.2140/agt.2011.11.2007

Mathematical Reviews number (MathSciNet)
MR2826931

Zentralblatt MATH identifier
1221.22008

Subjects
Primary: 22B05: General properties and structure of LCA groups
Secondary: 20E15: Chains and lattices of subgroups, subnormal subgroups [See also 20F22] 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 54D05: Connected and locally connected spaces (general aspects) 54F45: Dimension theory [See also 55M10]

Keywords
Chabauty topology locally compact abelian groups

Citation

Cornulier, Yves. On the Chabauty space of locally compact abelian groups. Algebr. Geom. Topol. 11 (2011), no. 4, 2007--2035. doi:10.2140/agt.2011.11.2007. https://projecteuclid.org/euclid.agt/1513715261


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