Topologies on the subgroup lattice of a compact group (Q1080534)
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scientific article; zbMATH DE number 3966493
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topologies on the subgroup lattice of a compact group |
scientific article; zbMATH DE number 3966493 |
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Topologies on the subgroup lattice of a compact group (English)
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1986
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It is proved that the Chabauty topology on the lattice \(\Sigma\) G of all closed subgroups of a compact group G coincides with the dual-Lawson topology iff the centre of G contains each connected subgroup (theorem 1). Repeating earlier results due to I. V. Protasov the author gives a criterion when \(\Sigma\) G is a topological lattice with respect to any of the two topologies.
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subgroup lattices
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Chabauty topology
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compact group
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dual-Lawson topology
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topological lattice
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