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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.
Authors: Arnautov Vladimir, G., N., Ermakova
Keywords: 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
– 0.27 Mb
Keywords: 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
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.V. I. Arnautov
Institute of Mathematics and Computer Science Vladimir
Andrunachevici
of the Moldova of State University
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail:
G. N. Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
Institute of Mathematics and Computer Science Vladimir
Andrunachevici
of the Moldova of State University
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail:
G. N. Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
DOI
https://doi.org/10.56415/basm.y2025.i1.p88Fulltext
– 0.27 Mb
Contents
- Generalized Berezin transform and Schatten class operators on weighted Bergman spaces
- Reverse Hardy inequalities via μ-proportional generalized fractional integral operators
- Some integrals for cosine families of bounded linear operators on some non-Archimedean Banach spaces
- About the Laplace transform on ${{L}^{1}}\left( \mathbb{R^+} \right)$
- Vertical Generalized Berger-type Metrics: A New Perspective on Harmonic Vector Fields
- On conharmonic curvature tensor of 6-dimensional planar Hermitian submanifolds of Cayley algebra
- 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.
- Pure and Mixed Stationary Equilibria for Dynamic Positional Games on Graphs
- On 4-T-quasigroups with exactly 20 distinct parastrophes
