Homeomorphisms of the space of non-zero integers with the Kirch topology

Yaryna Stelmakh

Анотація


The Golomb (resp. Kirch) topology on the set ℤ∙ of nonzero integers is generated by the base consisting of arithmetic progressions a+bℤ=a+bn:n∈ℤ where a∈ℤ∙ and b is a (square-free) number, coprime with a. In 2019 Dario Spirito proved that the space of nonzero integers endowed with the Golomb topology admits only two self-homeomorphisms.  In this paper we prove an analogous fact for the space of nonzero integers endowed with the Kirch topology: it also admits exactly two self-homeomorphisms.

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DOI: http://dx.doi.org/10.30970/vmm.2020.89.039-059

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