Increasing sequence of T0-topologies on the set of positive integers

被引：1

作者：

Krasinski, Dawid ^{[1
]}

Szyszkowska, Paulina ^{[1
]}

机构：

[1] Kazimierz Wielki Univ, Inst Math, Powstancow Wlkp 2, PL-85090 Bydgoszcz, Poland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2024年 / 341卷

关键词：

Topologies on N; Common division topology; Division topology; Connectedness; Locally connectedness; Arithmetic progressions; Prime numbers; Increasing sequence of topologies;

D O I：

10.1016/j.topol.2023.108732

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce, similarly as it was done in [11] for Kirch's type topologies, a sequence of topologies Tm that are subtopologies of the common division topology T. The sum of all topologies Tm is the common division topology. We also show that all topologies Tm are T0 and they are not T1 on N, examine properties of prime numbers and characterize connectedness of arithmetic progressions in each of the topology Tm. An immediate consequence of these characterizations is local connectedness of the space (N, Tm) for each m is an element of N. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：9

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