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Connections between connected topological spaces on the set of positive integers

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dc.contributor.author Szczuka, Paulina
dc.date.accessioned 2015-09-18T12:24:32Z
dc.date.available 2015-09-18T12:24:32Z
dc.date.issued 2013
dc.identifier.citation Open Mathematics 2013, Volume 11, Issue 5, Pages 876–881 en_US
dc.identifier.uri http://repozytorium.ukw.edu.pl/handle/item/1870
dc.description.abstract In this paper we introduce a connected topology T on the set ℕ 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 ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of the topological spaces (ℕ, T) and (ℕ, T′) en_US
dc.language.iso en en_US
dc.publisher De Gruyter Open en_US
dc.rights Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/pl/ *
dc.subject Division topology en_US
dc.subject Connectedness en_US
dc.subject Local connectedness en_US
dc.subject Arithmetic progression en_US
dc.title Connections between connected topological spaces on the set of positive integers en_US
dc.type Article en_US


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Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska Except where otherwise noted, this item's license is described as Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska