Constructing pseudo-τ-fine precompact groups

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-03-15 Epub Date: 2026-01-28 DOI:10.1016/j.topol.2026.109745

Dekui Peng , Gao Zhang

引用次数: 0

Abstract

Let τ be an uncountable cardinal. The notion of a τ-fine topological group was introduced by M.G. Tkachenko in 2021. More recently, H. Zhang et al. generalized this concept by defining pseudo-τ-fine topological groups to study certain factorization properties of continuous functions on topological groups. It is known that τ-fineness cannot coexist with precompactness in topological groups with uncountable character. In this paper, we investigate this problem further. We prove that, in topological groups with uncountable pseudocharacter, precompactness can coexist with pseudo-τ-fineness for some bounded τ but pseudocompactness can never.

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构造伪-τ-细预紧群

设τ为不可数基数。τ-fine拓扑群的概念是由M.G. Tkachenko在2021年提出的。最近，H. Zhang等人通过定义伪τ精细拓扑群来推广这一概念，研究了拓扑群上连续函数的某些分解性质。在具有不可数特征的拓扑群中，τ-精细性与预紧性不能共存。本文对这一问题进行了进一步的研究。证明了在具有不可数伪特征的拓扑群中，对于某些有界τ，预紧性可以与伪-τ-细性共存，但伪紧性不能共存。

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.