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Completeness of the factor group of a complete topological Abelian group by a discrete subgroup

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

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

Abstract: The factor group of a Hausdorff topological Abelian group by a discrete subgroup is complete iff the topological group is complete and the factor ring of a Hausdorff topological ring by a discrete ideal is complete iff the topological ring is complete.

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, complete topological ring.

MSC: 22A05

Received: 10.01.2024

Language: English

DOI: 10.56415/basm.y2024.i1-2.p137