21.107 (2026)

A sequence $\{F_n\}$ 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 $F_n \cap U \neq \varnothing$ 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.