On Metrics Inducing the Fürstenberg Topology on the Integers

2019/12/25 by Alexander Dirmeier, Dirmeier, Alexander
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1912.11663

openalex publication_date 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate various classes of metrics on the integers, which induce the Fürstenberg topology and establish the connection between the metrics and the topology. We analyze the norm-like mappings underlying these metrics, with respect to their efficient computability for natural numbers and the analytic behavior of sequences under those mappings. Subsequently, we give some applications to number theory and establish some new propositions at the intersection of number theory and topology.

Citations

• On an exotic topology of the integers

Related

• On an exotic topology of the integers
• Some topics related to metrics and norms, including ultrametrics and ultranorms, 2
• Metrics for Formal Structures, with an Application to Kripke Models and their Dynamics
• Generalized Metrics
• Finite metric spaces--combinatorics, geometry and algorithms