Connections between connected topological spaces on the set of positive integers |
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Authors: | Paulina Szczuka |
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Institution: | 1210. Institute of Mathematics, Kazimierz Wielki University, Pl. Weyssenhoffa 11, 85-072, Bydgoszcz, Poland
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Abstract: | In this paper we introduce a connected topology T on the set ? of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ? which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of the topological spaces (?, T) and (?, T′). |
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