Neighborhood system and categorical properties of quasitopological vector spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-02-18 DOI:10.1016/j.topol.2025.109281

Zhongqiang Yang , Yajing Fang , Qiunan Zheng

引用次数: 0

Abstract

With the background of diffeological vector spaces endowed with the D-topology, in the paper (Z. Yang and Z. Hu, 2024 [14]), the authors defined the concept of quasitopological vector space, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous and the scalar multiplication is continuous. Based on this, in the papers (Z. Yang and Y. Fang, 2024 [13]) and (Z. Yang and Q. Zheng, 2024 [15]), the authors continuously discussed this concept. In the present paper, we characterize the quasitopological vector space using the neighborhood system at 0, give the coproducts in the category of quasitopological vector spaces, and the free quasitopological vector space over any topological space.

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在D拓扑的衍射向量空间的背景下，作者在论文（杨泽和胡泽，2024 [14]）中定义了准拓扑向量空间的概念，即拓扑上满足向量加法分别连续和标量乘法连续条件的向量空间。在此基础上，作者在论文（杨泽和方颖，2024 [13]）和（杨泽和郑奇，2024 [15]）中连续讨论了这一概念。在本文中，我们利用 0 点邻域系统表征了准拓扑向量空间，给出了准拓扑向量空间范畴中的协积，以及任意拓扑空间上的自由准拓扑向量空间。

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.