Properties of arithmetics progressions in increasing sequence of T0-topologies on the set of positive integers

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-05-07 DOI:10.1016/j.topol.2024.108939

Dawid Krasiński, Paulina Szyszkowska

引用次数: 0

Abstract

In this paper we continue researches deal with increasing sequence ${T_{m}}$ of $T_{0}$ -topologies on the set of positive integers focusing on the properties of arithmetic progressions in topologies $T_{m}$ . We characterize the closures of arithmetic progressions in all topologies $T_{m}$ on $N$ . Additionally, we present the characterization of the closures of arithmetic progressions in the common division topology $T$ on $N$ . Moreover, for each $m \in N$ we characterize regular open arithmetic progressions in $(N, T_{m})$ and we examine which of these spaces are semiregular.

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正整数集合上 T0 拓扑递增序列中算术级数的性质

本文将继续研究正整数集合上 T0 拓扑的递增序列 {Tm}，重点是拓扑 Tm 中算术级数的性质。我们描述了 N 上所有拓扑 Tm 中算术级数的闭包。此外，我们还描述了 N 上常见分割拓扑 T 中算术级数的闭包。

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.

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