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 T. Banakh at Mathoverflow in 2017.
Keywords: Golomb topology; topologically rigid space
DOI: DOI 10.14712/1213-7243.2021.023
AMS Subject Classification: 11A99 54G15