2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137142It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian group embeds into a metrizable monothetic group. More generally, we describe all topological groups that can be embedded into monothetic groups: they are exactly abelian topological groups of weight $\leq\frak c$ covered by countably many translations of every nonempty open subset.10 pages, LaTeX 2eGeneral TopologyGroup Theory22A05text