Completeness of the factor group of a complete topological group and completeness of the factor ring of a complete topological ring by a compact normal subgroup and a compact ideal, respectively

V. I. Arnautov^a, G. N. Ermakova<sup>b

a</sup> Institute of Mathematics and Computer Science Vladimir Andrunachevici of the Moldova of State University, 5 Academiei str., MD-2028, Chisinau, Moldova
^b Transnistrian State University, 25 October str., 128, Tiraspol, 278000, Moldova

Abstract: If $M$ is a subgroup of an Abelian group $G(+)$ and $\tau$ is a group topology on the group $G$ such that $(G,\tau)$ is a complete topological group and $M$ is a compact or it is locally compact subgroup of the topological group $(G,\tau)$, then the factor group $(\overline G,\overline\tau)=(G,\tau)/M$ is a complete topological group.

Keywords and phrases: topological groups, topological rings, factor group of a topological group, factor ring of a topological ring, directed set, Cauchy sequence by a directed set, limit of a sequence by a directed set, complete topological group, Cauchy filter, complete topological ring.

MSC: 22A05

Received: 27.01.2025

Language: English

DOI: 10.56415/basm.y2025.i1.p88