Properties of the common division topology on the set of positive integers

被引：0

作者：

Szyszkowska, Paulina ^{[1
]}

Szyszkowski, Marcin ^{[1
]}

机构：

[1] Kazimierz Wielki Univ, Pl Weyssenhoffa 11, PL-85072 Bydgoszcz, Poland

来源：

JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY | 2018年 / 33卷 / 01期

关键词：

ARITHMETIC PROGRESSIONS; GOLOMBS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study properties of the common division topology T on the set of positive integers N. We prove that this space has the fixed point property. Moreover we characterize the Darboux property of polynomials which turns out to be equivalent to the continuity. In the last section we examine properties of prime numbers in the topology T.

引用

页码：91 / 98

页数：8

共 50 条

[1] Properties of the division topology on the set of positive integers
Szczuka, Paulina
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2016, 12 (03) : 775 - 785
[2] The closures of arithmetic progressions in the common division topology on the set of positive integers
Szczuka, Paulina
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2014, 12 (07): : 1008 - 1014
[3] The closures of arithmetic progressions in Kirch's topology on the set of positive integers
Szczuka, Paulina
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2015, 11 (03) : 673 - 682
[4] ON THE MEASURE ON THE SET OF POSITIVE INTEGERS
OKUTSU, K
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1993, 69 (06) : 173 - 174
[5] Substitutions and partitions of the set of positive integers
Tamura, JI
[J]. SUBSTITUTIONS IN DYNAMICS, ARITHMETICS AND COMBINATORICS, 2002, 1794 : 81 - 98
[6] Closure functions on the set of positive integers
岑嘉评
[J]. Science China Mathematics, 1996, (04) : 337 - 346
[7] Positive definite kernels on the set of integers, stability, some properties and applications
De La Barrera, Arnaldo
Ferrer, Osmin
Sanabria, Jose
[J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2022, 67 (04): : 841 - 854
[8] Closure functions on the set of positive integers
Shum, KP
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1996, 39 (04): : 337 - 346
[9] The common division topology on N
Alberto-Dominguez, Jose del Carmen
Acosta, Gerardo
Madriz-Mendoza, Maira
[J]. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2022, 63 (03): : 1 - 1
[10] Properties of increasing sequence of Kirch-type topologies on the set of positive integers
Szyszkowska, Paulina
[J]. TOPOLOGY AND ITS APPLICATIONS, 2022, 317

← 1 2 3 4 5 →