Classes of Baire spaces defined by semi-neighborhoods of the diagonal

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-25 DOI:10.1016/j.topol.2025.109556

Evgenii Reznichenko

引用次数: 0

Abstract

With the help of semi-neighborhoods of the diagonal, classes of Baire spaces are defined: Δ,

Δ_{h}

and

Δ_{s}

Baire spaces. These classes of spaces are studied with the help of topological games. They are useful in studying continuity in groups: paratopological Δ-Baire groups, quasi-topological

Δ_{h}

-Baire groups, and semitopological

Δ_{s}

-Baire groups are topological groups.

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由对角线的半邻域定义的贝尔空间类

利用对角线的半邻域，定义了贝尔空间的类：Δ、Δh和Δs。利用拓扑对策对这类空间进行了研究。它们在研究群中的连续性方面很有用：准拓扑Δ-Baire群、准拓扑Δh-Baire群和半拓扑Δs-Baire群都是拓扑群。

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.