21.103 (2026)

(V. V. Uspenskii). A Hausdorff topological group $G$ is called minimal if it does not admit a strictly coarser Hausdorff group topology. A topological group is called Raikov complete if its two-sided uniform structure is complete. It is known that a finite direct product of Raikov complete minimal topological groups is again minimal. Is it true that an arbitrary Cartesian product of Raikov complete minimal topological groups remains minimal?

It is known that an arbitrary Cartesian product of centre-free minimal topological groups is minimal (M. Megrelishvili, Topology Appl., 62, no. 1 (1995), 1–19).