On some relations between ideals of nowhere dense sets in topologies on positive integers

DOI10.1007/S10998-021-00426-6OpenAlexW3197685503WikidataQ114224913 ScholiaQ114224913MaRDI QIDQ2166163

Paulina Szyszkowska, Andrzej Nowik

Publication date: 23 August 2022

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-021-00426-6

zbMATH Keywords

arithmetic progressionsGolomb's topologyKirch's topologycommon division topologyFurstenberg's topologynowhere dense sets IdealsRizza's topology

Mathematics Subject Classification ID

Topological spaces and generalizations (closure spaces, etc.) (54A05) Connected and locally connected spaces (general aspects) (54D05) Density, gaps, topology (11B05) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Arithmetic progressions (11B25) Other combinatorial set theory (03E05) Primes (11A41)

Cites Work

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• Connections between connected topological spaces on the set of positive integers
• Ideals of nowhere dense sets in some topologies on positive integers
• The closures of arithmetic progressions in the common division topology on the set of positive integers
• Properties of the division topology on the set of positive integers
• The Darboux property for polynomials in Golomb’s and Kirch’s topologies
• On the Infinitude of Primes
• The closures of arithmetic progressions in Kirch's topology on the set of positive integers
• A Countable, Connected, Locally Connected Hausdorff Space
• A Connected Topology for the Integers

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