Disjoint Folner sequences in topological groups
Problem. A sequence {Fn } of pairwise disjoint finite subsets of a topological group is called expansive if for every open subset U there is a number m such that Fn ∩ U ̸= ∅ for all n > m. Suppose that a countable group G can be partitioned into countably many dense subsets. Is it true that in G there exists an expansive sequence? Cf. 15.80. This is Kourovka Notebook Problem \(21.107\).
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In TheoremDB, research kourovka-21-107-disjoint-folner-sequences-in-topological-groups: "Disjoint Folner sequences in topological groups". Call orient with problem_ref "kourovka-21-107-disjoint-folner-sequences-in-topological-groups", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- Outer order automorphisms of Dlab groupskourovka notebook
- Distributive lattices of right-relatively convex subgroupskourovka notebook
- Embedding groups of type F into higher finiteness typeskourovka notebook
How to cite
TheoremDB contributors, “Disjoint Folner sequences in topological groups,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-107-disjoint-folner-sequences-in-topological-groupsThis page as plain text: kourovka-21-107-disjoint-folner-sequences-in-topological-groups.md
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