Properties of increasing sequence of Kirch-type topologies on the set of positive integers

DOI10.1016/j.topol.2022.108188zbMath1504.54016OpenAlexW4283165290WikidataQ114127904 ScholiaQ114127904MaRDI QIDQ2161373

Paulina Szyszkowska

Publication date: 4 August 2022

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2022.108188

zbMATH Keywords

continuitypolynomialsarithmetic progressionsDarboux propertysemiregular spaceregular open setGolomb's topologyKirch-type topologyKirch's topology

Mathematics Subject Classification ID

Continuous maps (54C05) Polynomials in number theory (11C08) Topological spaces and generalizations (closure spaces, etc.) (54A05) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Arithmetic progressions (11B25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Cites Work

• Increasing sequence of topologies on the set of positive integers
• The Darboux property for polynomials in Golomb’s and Kirch’s topologies
• Regular open arithmetic progressions in connected topological spaces on the set of positive integers
• On the Infinitude of Primes
• Elementary Number Theory
• On continuous self-maps and homeomorphisms of the Golomb space
• A Countable, Connected, Locally Connected Hausdorff Space
• A Connected Topology for the Integers
• Unnamed Item

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