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ON THE CONNECTEDNESS OF THE CHABAUTY SPACE OF A LOCALLY COMPACT PRONILPOTENT GROUP

Part of: Locally compact groups and their algebras Fairly general properties Special aspects of infinite or finite groups Basic constructions

Published online by Cambridge University Press:  17 May 2021

BILEL KADRI Open the ORCID record for BILEL KADRI [Opens in a new window]
BILEL KADRI*
Affiliation:
Sfax Preparatory Engineering Institute, Department of Mathematics, Sfax University, 3018 Sfax, Tunisia
*
e-mail: [email protected]
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Abstract

Let G be a locally compact group and let ${\mathcal {SUB}(G)}$ be the hyperspace of closed subgroups of G endowed with the Chabauty topology. The main purpose of this paper is to characterise the connectedness of the Chabauty space ${\mathcal {SUB}(G)}$ . More precisely, we show that if G is a connected pronilpotent group, then ${\mathcal {SUB}(G)}$ is connected if and only if G contains a closed subgroup topologically isomorphic to ${{\mathbb R}}$ .

Keywords

Chabauty topologylocally compact grouppronilpotent group

MSC classification

Primary: 54B20: Hyperspaces
Secondary: 20F19: Generalizations of solvable and nilpotent groups 22D05: General properties and structure of locally compact groups 54D05: Connected and locally connected spaces (general aspects)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 161 - 170
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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