Weak König’s Lemma Implies the Uniform Continuity Theorem

Abstract

As the title suggests we are going to show that Weak König’s Lemma implies the uniform continuity theorem; to be more precise the uniform continuity theorem for functions $[0,1] \to \R$ . This improves upon a result by J. Berger who has proven this implication for functions $[0,1] \to \N$ .