A continuity principle equivalent to the monotone $\Pi^{0}_{1}$ fan theorem

TL;DR

This paper establishes an equivalence between a strong continuity principle in constructive mathematics and the fan theorem for monotone $\

Contribution

It demonstrates the equivalence of a continuity principle with a classical fan theorem within constructive reverse mathematics.

Findings

The strong continuity principle is equivalent to the fan theorem for monotone $\

The work is conducted in the framework of constructive reverse mathematics.

The paper provides a new perspective on the relationship between continuity principles and classical theorems.

Abstract

The strong continuity principle reads "every pointwise continuous function from a complete separable metric space to a metric space is uniformly continuous near each compact image." We show that this principle is equivalent to the fan theorem for monotone $\Pi^{0}_{1}$ bars. We work in the context of constructive reverse mathematics.