右半拓扑群中运算的连续性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-14 DOI:10.1016/j.topol.2024.108952

Evgenii Reznichenko

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引用次数: 0

摘要

我们考虑的是具有拓扑结构的群，这种拓扑结构与代数结构在某种程度上是一致的。具有拓扑结构的著名群类有拓扑群、准拓扑群、半拓扑群和准拓扑群。我们还研究了拓扑和代数结构的其他匹配方式。本文的最低要求是群是右半拓扑群（此类群通常称为右拓扑群）。我们研究具有拓扑结构的群何时是拓扑群；这方面的研究始于迪恩-蒙哥马利和罗伯特-埃利斯的工作。(对角线的（不变）半邻域被用作一种研究手段。

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Continuity of operations in right semitopological groups

Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Well-known classes of groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study other ways of matching topology and algebraic structure. The minimum requirement in this paper is that the group is a right semitopological group (such groups are often called right topological groups). We study when a group with a topology is a topological group; research in this direction began with the work of Deane Montgomery and Robert Ellis. (Invariant) semi-neighborhoods of the diagonal are used as a means of study.

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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.