Coset topologies on $\mathbb{Z}$ and arithmetic applications
Number Theory
2022-11-28 v3 General Topology
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 , obtained from closed sets of the profinite completion . We also discuss various applications to number theory.
Cite
@article{arxiv.2202.13478,
title = {Coset topologies on $\mathbb{Z}$ and arithmetic applications},
author = {Ignazio Longhi and Yunzhu Mu and Francesco Maria Saettone},
journal= {arXiv preprint arXiv:2202.13478},
year = {2022}
}
Comments
Final version; to appear in Expositiones Mathematicae