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Journal of the Ramanujan Mathematical Society

Volume 33, Issue 1, March 2018  pp. 91–98.

Properties of the common division topology on the set of positive integers

Authors:  Paulina Szyszkowska and Marcin Szyszkowski
Author institution:Kazimierz Wielki University, pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Summary:  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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