On partitions of groups into dense subsets (Q1867189)
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scientific article; zbMATH DE number 1891215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On partitions of groups into dense subsets |
scientific article; zbMATH DE number 1891215 |
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On partitions of groups into dense subsets (English)
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2 April 2003
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A group is called absolutely resolvable (absolutely \(\omega\)-resolvable) if it can be partitioned into two (into \(\omega)\) subsets dense in any nondiscrete group topology. The author proves the basic theorems: (1) Every countable \(\omega\)-irresolvable topological group contains an open Boolean subgroup. (2) Every countable group with finitely many elements of order 2, that can be embedded in a compact topological group, is absolutely \(\omega\)-resolvable.
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resolvability
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local left topological group
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local automorphism
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topological group
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