Topologies on the subgroup lattice of a compact group

Scheiderer, Claus

doi:10.1016/0166-8641(86)90040-4

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Lattice Topologies1

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2023

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Cited by 3 publications

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“…More on the lattices topologies on L(G) in the case of a compact G can be find in [46]. These topologies are studied in [47] • for every U ∈ Σ(H), there exists V ∈ Σ(H) such that U ∈ Σ(K) for each K ∈ L(G), K ⊆ V;…”

Section: Lattice Topologiesmentioning

confidence: 99%

Selective Survey on Spaces of Closed Subgroups of Topological Groups

Протасов¹

2018

Axioms

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Section: Lattice Topologiesmentioning

confidence: 99%

Selective Survey on Spaces of Closed Subgroups of Topological Groups

Протасов¹

2018

Axioms

View full text Add to dashboard Cite

show abstract

Closed subgroups of compact groups having open Chabauty spaces

Alaya,

Hamrouni,

Jlali

2023

Proc Math Sci

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Locally compact groups with totally disconnected space of subgroups

Hamrouni

Kadri

2018

Journal of Group Theory

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The closed subsets {\mathcal{F}(X)} of any topological space can be given a topology, called the Chabauty–Fell topology, in which {\mathcal{F}(X)} is quasi-compact. If X is a locally compact space, then {\mathcal{F}(X)} is Hausdorff. If {X=G} is a locally compact group, then the subset {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} of closed subgroups is closed in {\mathcal{F}(G)} , and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in this paper deal with the following question: Given a locally compact topological group, when is {\mathcal{F}(G)} (resp. {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} ) a totally disconnected space?

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Topologies on the subgroup lattice of a compact group

Cited by 3 publications

References 9 publications

Selective Survey on Spaces of Closed Subgroups of Topological Groups

Selective Survey on Spaces of Closed Subgroups of Topological Groups

Closed subgroups of compact groups having open Chabauty spaces

Locally compact groups with totally disconnected space of subgroups

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