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arXiv · 2202.13478

Coset topologies on $\mathbb{Z}$ and arithmetic applications

Ignazio Longhi·Yunzhu Mu·Francesco Maria Saettone
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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 $\mathbb{Z}$, obtained from closed sets of the profinite completion $\hat{\mathbb{Z}}$. We also discuss various applications to number theory.

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Ignazio Longhi, Yunzhu Mu, Francesco Maria Saettone. 2022-02-27. Coset topologies on $\mathbb{Z}$ and arithmetic applications. https://doi.org/10.1016/j.exmath.2022.10.001

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