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On the connectedness of the Chabauty space of a locally compact prosolvable group
-
Hatem Hamrouni
and
Bilel Kadri
Published/Copyright:
March 18, 2015
Abstract
Let G be a locally compact group. We denote by 𝒮𝒰ℬ(ℝ × G) the hyperspace of closed subgroups of ℝ × G endowed with the Chabauty topology. In this paper, some general results about the connectedness of the hyperspace 𝒮𝒰ℬ(ℝ × G) are established. The main result proved here is that if G is a prosolvable group, then 𝒮𝒰ℬ(ℝ × G) is connected. We also prove a partial converse to the result just mentioned.
We thank Professor Yves de Cornulier for suggesting us this problem. It is great pleasure to thank Professor Karl Heinrich Hofmann for pointing out numerous references related to this work. We thank the anonymous referee for his/her detailed comments that helped to increase the quality of the paper.
Received: 2014-7-19
Revised: 2014-11-26
Accepted: 2015-1-7
Published Online: 2015-3-18
Published in Print: 2015-4-1
© 2015 by De Gruyter
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- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
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Keywords for this article
Locally compact group;
Chabauty topology;
strong projective limit;
prosolvable group
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
- Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
- The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
