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ON THE CONNECTEDNESS OF THE CHABAUTY SPACE OF A LOCALLY COMPACT PRONILPOTENT GROUP
Part of:
Basic constructions
Special aspects of infinite or finite groups
Fairly general properties
Locally compact groups and their algebras
Published online by Cambridge University Press: 17 May 2021
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 ${{\mathbb R}}$ .
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 161 - 170
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
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