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 ${{\mathbb R}}$ .

中文翻译：

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关于本地紧凑型 Pronilpotent Group 的 CHABAUTY 空间的连通性

让G是一个局部紧群并且让${\mathcal {SUB}(G)}$是闭子群的超空间G具有 Chabauty 拓扑。本文的主要目的是刻画Chabauty空间的连通性${\mathcal {SUB}(G)}$. 更准确地说，我们证明如果G是连通的全能群，则${\mathcal {SUB}(G)}$当且仅当G包含一个拓扑同构的封闭子群${{\mathbb R}}$.