In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.
@article{bwmeta1.element.doi-10_2478_s11533-013-0394-6,
author = {Paulina Szczuka},
title = {The closures of arithmetic progressions in the common division topology on the set of positive integers},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1008-1014},
zbl = {1304.54007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0394-6}
}
Paulina Szczuka. The closures of arithmetic progressions in the common division topology on the set of positive integers. Open Mathematics, Tome 12 (2014) pp. 1008-1014. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0394-6/
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