Group topologies on the integers generated by sequences

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-16 DOI:10.1016/j.topol.2024.109102

Lydia Außenhofer , Dikran Dikranjan

引用次数: 0

Abstract

In the first part of the paper we study various ways to introduce a group topology on the group

Z

of integers by using sequences of natural numbers b, among them the well-known Protasov-Zelenyuk topology

T_{b}

for a T-sequence b. We prove, among others, that for slowly diverging sequences b, the group

(Z, T_{b})

is not locally quasi-convex, in particular not reflexive. As an application, in the second part we resolve Problem 6.1 and Problem 6.5 from [28].

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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.