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

Tatsuji Kawai

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arXiv · 1808.08076

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

Tatsuji Kawai

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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.

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Tatsuji Kawai. 2018-08-24. A continuity principle equivalent to the monotone $\Pi^{0}_{1}$ fan theorem. https://arxiv.org/abs/1808.08076

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