Weakly first-countability in strongly topological gyrogroups

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-04-20 DOI:10.1016/j.topol.2024.108920

Jing Zhang , Kaixiong Lin , Wenfei Xi

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Abstract

In this note, it is proved that (1) if $(G, τ, \oplus)$ is a strongly topological gyrogroup and H is a closed strong subgyrogroup of G, then $G / H$ is κ-Fréchet-Urysohn if and only if $G / H$ is strongly κ-Fréchet-Urysohn under the condition that H is neutral; (2) let H be a closed strong subgyrogroup of a strongly topological gyrogroup $(G, τ, \oplus)$ , then the equality $Δ (G / H) = ψ (G / H)$ holds when H is neutral; (3) if $(G, τ, \oplus)$ is a sequential strongly topological gyrogroup having a point-countable k-network, then G is metrizable or a topological sum of cosmic subspaces. There results improve the related results in topological groups.

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强拓扑陀螺群中的弱第一可计算性

本注解证明：(1) 若 (G,τ,⊕) 是强拓扑陀螺群，且 H 是 G 的封闭强子陀螺群，则当且仅当 G/H 在 H 是中性的条件下是强 κ-Fréchet-Urysohn 时，G/H 才是κ-Fréchet-Urysohn；(2) 设 H 是强拓扑陀螺群(G,τ,⊕)的封闭强子陀螺群，则当 H 是中性时，等式 Δ(G/H)=ψ(G/H)成立；(3) 若(G,τ,⊕)是具有可计点 k 网的连续强拓扑陀螺群，则 G 是可元空间或宇宙子空间的拓扑和。这些结果改进了拓扑群的相关结果。

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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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