The Golomb topology of polynomial rings, II

Abstract

We study the interplay of the Golomb topology and the algebraic structure in polynomial rings K[X] over a field K. In particular, we focus on infinite fields K of positive characteristic such that the set of irreducible polynomials of K[X] is dense in the Golomb space G(K[X]). We show that, in this case, the characteristic of K is a topological invariant, and that any self-homeomorphism of G(K[X]) is the composition of multiplication by a unit and a ring automorphism of K[X].