• Corpus ID: 252531950

# The Golomb topology of polynomial rings, II

@inproceedings{Spirito2022TheGT,
title={The Golomb topology of polynomial rings, II},
author={Dario Spirito},
year={2022}
}
. 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 ].

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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 $\{a+bn\}_{n=0}^\infty$ with

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