Embeddings into monothetic groups (Q721694)

In [J. Group Theory. 3, No. 4, 407--417 (2000; Zbl 0961.22002)], \textit{S. A. Morris} and \textit{V. Pestov} showed that every separable abelian topological group can be embedded into a monothetic group. The author of the paper under this review proves the following theorem. Theorem. Let \(G\) be a separable abelian group with a bounded invariant metric \(d\). Then \(d\) extends to a (bounded by the same constant) metric \(D\) on \(G\oplus C\), where \(C\) is a cyclic group which is dense in \(G\oplus C\). In particular, \(G\) embeds into a monothetic group. The result of Morris and Pestov [loc. cit.] is an immediate corollary of this theorem.