Strongly topologically orderable gyrogroups with a suitable set

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-02 DOI:10.1016/j.topol.2025.109565

Jiamin He , Jiajia Yang , Fucai Lin

引用次数: 0

Abstract

A discrete subset S of a topologically gyrogroup G is called a suitable set for G if

S \cup {1}

is closed and the subgyrogroup generated by S is dense in G, where 1 is the identity element of G. In this paper, we mainly study the existence of suitable set of strongly topologically orderable gyrogroups, which extends some result in some papers in the literature. In particular, the existences of suitable set of each locally compact or not totally disconnected strongly topologically orderable gyrogroup are affirmative.

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具有合适集合的强拓扑可序陀螺群

如果S∪{1}是闭的，且S生成的子陀螺群在G中是稠密的，则S的离散子集S称为G的适宜集，其中1是G的单位元。本文主要研究了强拓扑可序陀螺群适宜集的存在性，推广了文献中一些文章的结果。特别是，各局部紧或不完全断开的强拓扑可序陀螺群的合适集的存在性是肯定的。

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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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.