2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126977It is proved that the continuum hypothesis implies the existence of a group M containing a nonalgebraic unconditionally closed set, i.e., a set which is closed in any Hausdorff group topology on M but is not an intersection of finite unions of solution sets of equations in M.Version 2: The proof is made much more detailed. Several misprints are correctedGroup TheoryGeneral Topology22A05 (Primary); 54H11 (Secondary)text