# The closures of arithmetic progressions in the common division topology on the set of positive integers

Open Mathematics (2014)

- Volume: 12, Issue: 7, page 1008-1014
- ISSN: 2391-5455

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topPaulina Szczuka. "The closures of arithmetic progressions in the common division topology on the set of positive integers." Open Mathematics 12.7 (2014): 1008-1014. <http://eudml.org/doc/269569>.

@article{PaulinaSzczuka2014,

abstract = {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.},

author = {Paulina Szczuka},

journal = {Open Mathematics},

keywords = {The common division topology; Closures; Arithmetic progressions; the common division topology; closures; arithmetic progressions},

language = {eng},

number = {7},

pages = {1008-1014},

title = {The closures of arithmetic progressions in the common division topology on the set of positive integers},

url = {http://eudml.org/doc/269569},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Paulina Szczuka

TI - The closures of arithmetic progressions in the common division topology on the set of positive integers

JO - Open Mathematics

PY - 2014

VL - 12

IS - 7

SP - 1008

EP - 1014

AB - 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.

LA - eng

KW - The common division topology; Closures; Arithmetic progressions; the common division topology; closures; arithmetic progressions

UR - http://eudml.org/doc/269569

ER -

## References

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- [8] Szczuka P., The connectedness of arithmetic progressions in Furstenberg’s, Golomb’s, and Kirch’s topologies, Demonstratio Math., 2010, 43(4), 899–909 Zbl1303.11021
- [9] Szczuka P., Connections between connected topological spaces on the set of positive integers, Cent. Eur. J. Math., 2013, 11(5), 876–881 http://dx.doi.org/10.2478/s11533-013-0210-3 Zbl1331.54021
- [10] Szczuka P., Regular open arithmetic progressions in connected topological spaces on the set of positive integers, Glas. Mat. (in press) Zbl06374862