Almost periodic functions, constructively

TL;DR

This paper provides a constructive proof of Bohr's fundamental theorem for almost periodic functions, extending it to functions on general topological groups, addressing challenges in constructive mathematics.

Contribution

It offers a simple constructive proof of Bohr's theorem and generalizes it to almost periodic functions on topological groups, a novel approach in constructive mathematics.

Findings

Constructive proof of Bohr's fundamental theorem

Extension to almost periodic functions on topological groups

Addresses non-separability in constructive analysis

Abstract

The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.