On topological properties of the formal power series substitution group
Ivan Konstantinovich Babenko, S. Bogatyi · L’Enseignement Mathématique · 2014
Certain topological properties of the group \mathcal J(\bf k) of formal one-variable power series with coefficients in a commutative topological unitary ring \bf k are considered. We show, in particular, that in the case of \bf k=\mathbb Z equipped with the discrete topology, in spite of the fact that the group \mathcal J(\mathbb Z) has continuous monomorphisms into compact groups, it cannot be embedded into a locally compact group. In the case where \bf k=\mathbb Q the group \mathcal J(\mathbb Q) has no continuous monomorphisms into a locally compact group. In the last part of the paper the compressibility property for topological groups is considered. This property is valid for \mathcal J(\bf k) for a number of rings, in particular for the group \mathcal J(\mathbb Z) .