射影正则（T2，T1）弱可发展半坡群

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-07-30 DOI:10.1016/j.topol.2024.109028

Vikesh Kumar , Brij Kishore Tyagi

引用次数: 0

摘要

本文介绍了弱平衡半坡群的概念，并证明弱平衡半坡群类在取子群和积的情况下是封闭的。本文证明，正则（Hausdorff, ）半坡群允许作为子群同构嵌入到正则（Hausdorff, ）半坡群的具有弱发展的乘积中，当且仅当弱平衡且（, ）时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Projectively regular (T2, T1) weakly developable semitopological groups

In this paper, we introduce the notion of weakly ω-balanced semitopological groups and prove that the class of weakly ω-balanced semitopological groups is closed under taking subgroups and products. It is prove that a regular (Hausdorff, $T_{1}$ ) semitopological group G admits a homeomorphic embedding as a subgroup into a product of regular (Hausdorff, $T_{1}$ ) semitopological groups with a weak development if and only if G is weakly ω-balanced and $I r (G) \leq ω$ ( $H s (G) \leq ω$ , $S m (G) \leq ω$ ).

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.

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