  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.
