Weak K\"{o}nig's lemma implies the uniform continuity theorem: a direct proof

TL;DR

This paper provides a direct constructive proof that weak K"onig's lemma implies the uniform continuity theorem within Bishop's constructive mathematics, utilizing countable choice.

Contribution

It establishes a new constructive connection between weak K"onig's lemma and the uniform continuity theorem with a direct proof approach.

Findings

Weak K"onig's lemma implies the uniform continuity theorem in Bishop's constructive mathematics.

The proof uses countable choice within a constructive framework.

Provides a constructive alternative to classical implications.

Abstract

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.