The generalized metric property in strongly topological gyrogroups

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-22 DOI:10.1016/j.topol.2024.109046

Meng Bao, Xiaolan Liu

引用次数: 0

Abstract

A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. It is shown that a strongly topological gyrogroup is a q-space if and only if it is an M-space. Then a characterization about weakly feathered strongly topological gyrogroups is given, that is, a strongly topological gyrogroup G is weakly feathered if and only if it contains a compact strong subgyrogroup H such that the quotient space $G / H$ is submetrizable.

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强拓扑陀螺群中的广义度量属性

拓扑陀螺群是具有拓扑结构的陀螺群，其二元操作是连续的，反映射也是连续的。研究表明，强拓扑陀螺群是一个 q 空间，当且仅当它是一个 M 空间。然后给出了一个关于弱羽化强拓扑陀螺群的特征，即强拓扑陀螺群 G 是弱羽化的，当且仅当它包含一个紧凑的强子陀螺群 H，使得商空间 G/H 是可亚对称的。

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.