Coset topologies on Z and arithmetic applications

Ignazio Longhi; Yunzhu Mu; Francesco Maria Saettone

doi:10.1016/j.exmath.2022.10.001

Coset topologies on Z and arithmetic applications

Ignazio Longhi
, Yunzhu Mu
, Francesco Maria Saettone

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies on Z, obtained from closed sets of the profinite completion Zˆ. We also discuss various applications to number theory.

Original language	English
Pages (from-to)	71-114
Number of pages	44
Journal	Expositiones Mathematicae
Volume	41
Issue number	1
DOIs	https://doi.org/10.1016/j.exmath.2022.10.001
State	Published - 1 Mar 2023

Keywords

Closed subsets of Zˆ
Coset topologies
Counting prime functions
Pathological topological spaces
Supernatural numbers

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.exmath.2022.10.001

Cite this

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title = "Coset topologies on Z and arithmetic applications",

abstract = "We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies on Z, obtained from closed sets of the profinite completion Zˆ. We also discuss various applications to number theory.",

keywords = "Closed subsets of Zˆ, Coset topologies, Counting prime functions, Pathological topological spaces, Supernatural numbers",

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AU - Longhi, Ignazio

AU - Mu, Yunzhu

AU - Saettone, Francesco Maria

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N2 - We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies on Z, obtained from closed sets of the profinite completion Zˆ. We also discuss various applications to number theory.

AB - We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies on Z, obtained from closed sets of the profinite completion Zˆ. We also discuss various applications to number theory.

KW - Closed subsets of Zˆ

KW - Coset topologies

KW - Counting prime functions

KW - Pathological topological spaces

KW - Supernatural numbers

UR - https://www.scopus.com/pages/publications/85143865615

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DO - 10.1016/j.exmath.2022.10.001

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VL - 41

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EP - 114

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 1

ER -

Coset topologies on Z and arithmetic applications

Abstract

Keywords

ASJC Scopus subject areas

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