Additive subgroups of real vector spaces and topologies on them

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-30 DOI:10.1016/j.topol.2025.109488

Batoul Yousefipour , S. Sajjad Gashti , Hassan Myrnouri

引用次数: 0

Abstract

In the present paper, we study group topologies on torsion free abelian groups and real vector spaces. We introduce the concept of Q-balanced subsets of a torsion free abelian group. Absorbed elements of a real vector space equipped with a group topology (with addition) is another concept that is presented.

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实向量空间的加性子群及其上的拓扑

本文研究了无扭阿贝尔群和实向量空间上的群拓扑。引入无扭阿贝尔群的q平衡子集的概念。实向量空间中具有群拓扑（带加法）的吸收元素是另一个概念。

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.