The closures of arithmetic progressions in the common division topology on the set of positive integers

DOI10.2478/S11533-013-0394-6zbMath1304.54007OpenAlexW2051031732MaRDI QIDQ2248499

Paulina Szczuka

Publication date: 26 June 2014

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-013-0394-6

zbMATH Keywords

arithmetic progressionsclosuresthe common division topology

Mathematics Subject Classification ID

Topological spaces and generalizations (closure spaces, etc.) (54A05) Arithmetic progressions (11B25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Primes (11A41)

Related Items (5)

On some relations between ideals of nowhere dense sets in topologies on positive integers ⋮ Unnamed Item ⋮ Coset topologies on \(\mathbb{Z}\) and arithmetic applications ⋮ Ideals of nowhere dense sets in some topologies on positive integers ⋮ The common division topology on $\mathbb{N}$

Cites Work

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• Connections between connected topological spaces on the set of positive integers
• Regular open arithmetic progressions in connected topological spaces on the set of positive integers
• On the Infinitude of Primes
• A Countable, Connected, Locally Connected Hausdorff Space
• A Connected Topology for the Integers

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