Journal of the Ramanujan Mathematical Society

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Properties of the Common Division Topology on the Set of Positive Integers


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1 Kazimierz Wielki University, Pl. Weyssenhoffa 11, 85–072 Bydgoszcz, Poland
     

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We study properties of the common division topology T on the set of positive integers N. We prove that this space has the fixed point property. Moreover we characterize the Darboux property of polynomials which turns out to be equivalent to the continuity. In the last section we examine properties of prime numbers in the topology T.
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  • Properties of the Common Division Topology on the Set of Positive Integers

Abstract Views: 214  |  PDF Views: 1

Authors

Paulina Szyszkowska
Kazimierz Wielki University, Pl. Weyssenhoffa 11, 85–072 Bydgoszcz, Poland
Marcin Szyszkowski
Kazimierz Wielki University, Pl. Weyssenhoffa 11, 85–072 Bydgoszcz, Poland

Abstract


We study properties of the common division topology T on the set of positive integers N. We prove that this space has the fixed point property. Moreover we characterize the Darboux property of polynomials which turns out to be equivalent to the continuity. In the last section we examine properties of prime numbers in the topology T.

References