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- W4224021285 abstract "In this paper we deal with topologies defined on the set of positive integers. We introduce a sequence of topologies Dm that are subtopologies of Golomb's topology D. The sum of all topologies Dm is Golomb's topology. We show also that all topologies Dm are Haudsdorff but not regular on N. Further, we characterize connectedness of arithmetic progressions in each topology Dm. An immediate consequence of these characterizations is local connectedness of the space (N,Dm) for each m∈N." @default.
- W4224021285 created "2022-04-19" @default.
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- W4224021285 date "2022-06-01" @default.
- W4224021285 modified "2023-10-03" @default.
- W4224021285 title "Increasing sequence of topologies on the set of positive integers" @default.
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- W4224021285 doi "https://doi.org/10.1016/j.topol.2022.108096" @default.
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