The Golomb space is topologically rigid

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.

8 pages

Cited by in corpus (2)

• Coset topologies on $\mathbb{Z}$ and arithmetic applications
• The Macias topology on integral domains