拓扑群和弱拓扑群中的广义元可性质概览

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-09 DOI:10.1016/j.topol.2024.108944

Shou Lin , Xuewei Ling , Xin Liu

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引用次数: 0

摘要

广义元可空间理论是广义拓扑学的一个重要课题。本文是对拓扑群和弱拓扑群中广义可元空间性质的研究方法和成果的综述。我们主要研究了拓扑群、半拓扑群、准拓扑群、准拓扑群和自由拓扑群中的这类性质，并重点讨论了分离性质的影响、弱拓扑群成为拓扑群的条件、卡底不变式、弱第一可计算性、三空间性质和拓扑群上压实中的余数以及相关结构。最后，为研究人员列出了这一领域的一些未决问题。

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A survey of generalized metrizable properties in topological groups and weakly topological groups

The theory of generalized metrizable spaces is an important topic of general topology. This paper is a survey of research methods and achievements on generalized metrizable properties in topological groups and weakly topological groups. We mainly study this kind of properties in topological groups, semitopological groups, paratopological groups, quasitopological groups and free topological groups, and focus on the influence of separation properties, conditions for weakly topological groups to become topological groups, cardinal invariants, weak first-countability, three-space properties and remainders in compactifications on topological groups and related structures. Finally, some unsolved problems in this field are listed for researchers.

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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.