Compactification l-adique de R

TL;DR

The paper constructs a compact topological group containing both real and l-adic groups as dense subgroups, providing an arithmetic perspective on the l-adic solenoid.

Contribution

It introduces a new compactification of the real line that incorporates the l-adic numbers, linking topology and number theory.

Findings

The group Rl is a compact topological group containing R and Ql densely.

Provides an arithmetic interpretation of the l-adic solenoid.

Studies properties of the constructed group Rl.

Abstract

We construct a compact topological group Rl which contains both the real additive group R and the l-adic one Ql (for a given prime number l) as dense subgroups; thus we study some of its properties. This construction gives an arithmetic description of the so-called l-adic solenoid classically defined in terms of foliations.