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Keywords:
Golomb topology; topologically rigid space
Golomb topology; topologically rigid space
Summary:
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.
References:
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