The Darboux property for polynomials in Golomb’s and Kirch’s topologies

DOI10.1515/DEMA-2013-0454zbMath1303.54004OpenAlexW911246494MaRDI QIDQ2860792

Paulina Szczuka

Publication date: 11 November 2013

Published in: Demonstratio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/dema-2013-0454

zbMATH Keywords

continuitypolynomialsarithmetic progressionsDarboux propertyGolomb's topologyKirch's topology

Mathematics Subject Classification ID

Continuous maps (54C05) Special maps on topological spaces (open, closed, perfect, etc.) (54C10) Polynomials in number theory (11C08)

Related Items (7)

Golomb's arithmetical semigroup topology and a semiprime sufficiency condition for Dirichlet's theorem ⋮ Properties of increasing sequence of Kirch-type topologies on the set of positive integers ⋮ On some relations between ideals of nowhere dense sets in topologies on positive integers ⋮ Unnamed Item ⋮ The Kirch space is topologically rigid ⋮ On some generalizations of the Kirch's ideal ⋮ On continuous self-maps and homeomorphisms of the Golomb space

Cites Work

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• On the Infinitude of Primes
• Adic Topologies for the Rational Integers
• A Countable, Connected, Locally Connected Hausdorff Space
• A Connected Topology for the Integers
• A connected countable Hausdorff space

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