# Disjoint Folner sequences in topological groups

- Reference: `kourovka-21-107-disjoint-folner-sequences-in-topological-groups`
- Page: https://theoremdb.org/statements/kourovka-21-107-disjoint-folner-sequences-in-topological-groups
- Record maturity: Reviewed problem

## 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 \(21.107\).

## Status

The reviewed record remains open.

## Work

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `kourovka-21-107-disjoint-folner-sequences-in-topological-groups`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.