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arXiv · 1912.01994

The Golomb space is topologically rigid

Taras Banakh·Dario Spirito·Sławomir Turek
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Abstract

The $Golomb$ $space$ $\mathbb N_\tau$ is the set $\mathbb N$ of positive integers endowed with the topology $\tau$ generated by the base consisting of arithmetic progressions $\{a+bn:n\ge 0\}$ with coprime $a,b$. We prove that the Golomb space $\mathbb N_\tau$ is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by the first author at Mathoverflow in 2017.

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Taras Banakh, Dario Spirito, Sławomir Turek. 2019-12-04. The Golomb space is topologically rigid. https://doi.org/10.14712/1213-7243.2021.023

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