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arXiv · 2209.12594

The Golomb topology of polynomial rings, II

Dario Spirito
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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 $K[X]$.

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Dario Spirito. 2022-09-26. The Golomb topology of polynomial rings, II. https://arxiv.org/abs/2209.12594

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