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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