Geodesic
The Golomb space is topologically rigid
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 347-360.

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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 T. Banakh at Mathoverflow in 2017.
DOI : 10.14712/1213-7243.2021.023
Classification : 11A99, 54G15
Keywords: Golomb topology; topologically rigid space 
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Banakh, Taras; Spirito, Dario; Turek, Sławomir. The Golomb space is topologically rigid. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 347-360. doi : 10.14712/1213-7243.2021.023. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.023/

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