A continuity principle equivalent to the monotone ${\Pi }_1^0$ fan theorem

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 ${\Pi }_1^0$ bars. We work in the context of constructive reverse mathematics.

arXiv comment13 pages