F ¯ p as a Discrete Metric Space

Abstract

We define a metric that makes the algebraic closure of a finite field [Formula: see text] into a UDBG (uniformly discrete with bounded geometry) metric space. This metric stems from algebraic properties of [Formula: see text]. From this perspective, for [Formula: see text] we explore common research themes in metric spaces, reveal how peculiar properties naturally arise, and present it as a new type of example for certain well-studied questions.