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- W4387142721 abstract "In this paper we introduce, similarly as it was done in [11] for Kirch's type topologies, a sequence of topologies Tm that are subtopologies of the common division topology T. The sum of all topologies Tm is the common division topology. We also show that all topologies Tm are T0 and they are not T1 on N, examine properties of prime numbers and characterize connectedness of arithmetic progressions in each of the topology Tm. An immediate consequence of these characterizations is local connectedness of the space (N,Tm) for each m∈N." @default.
- W4387142721 created "2023-09-29" @default.
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- W4387142721 date "2024-01-01" @default.
- W4387142721 modified "2023-10-18" @default.
- W4387142721 title "Increasing sequence of T0-topologies on the set of positive integers" @default.
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- W4387142721 doi "https://doi.org/10.1016/j.topol.2023.108732" @default.
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