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 Z. We also discuss various applications to number theory.(c) 2022 Elsevier GmbH. All rights reserved.
Coset topologies on and arithmetic applications
Ignazio Longhi;Francesco Maria Saettone
2023-01-01
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 Z. We also discuss various applications to number theory.(c) 2022 Elsevier GmbH. All rights reserved.
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