Properties of the division topology on the set of positive integers-Reference-Cited by-同舟云学术

Properties of the division topology on the set of positive integers

Published:2016-03-23 Issue:03 Volume:12 Page:775-785
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Szczuka Paulina¹

Affiliation:

1. Department of Mathematics, Kazimierz Wielki University, pl. Weyssenhoffa 11, Bydgoszcz 85–072, Poland

Abstract

In this paper, we examine properties of the division topology on the set of positive integers introduced by Rizza in 1993. The division topology on [Formula: see text] with the division order is an example of [Formula: see text]-Alexandroff topology. We mainly concentrate on closures of arithmetic progressions and connected and compact sets. Moreover, we show that in the division topology on [Formula: see text], the continuity is equivalent to the Darboux property.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116500500

Reference15 articles.

1. On the Infinitude of Primes

2. A Connected Topology for the Integers

3. A Countable, Connected, Locally Connected Hausdorff Space

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