Glasnik Matematicki, Vol. 49, No. 1 (2014), 13-23.

REGULAR OPEN ARITHMETIC PROGRESSIONS IN CONNECTED TOPOLOGICAL SPACES ON THE SET OF POSITIVE INTEGERS

Paulina Szczuka

Department of Mathematics, Kazimierz Wielki University, pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
e-mail: paulinaszczuka@wp.pl


Abstract.   In this paper we characterize regular open arithmetic progressions in four connected topological spaces on the set of positive integers with bases consisting of some arithmetic progressions and we examine which of these spaces are semiregular.

2010 Mathematics Subject Classification.   11B25, 54A05, 11A41.

Key words and phrases.   Furstenberg's topology, Golomb's topology, Kirch's topology, the division topology, arithmetic progressions, regular open set, semiregular space.


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DOI: 10.3336/gm.49.1.02


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