A continuity principle equivalent to the monotone Π⁰₁ fan theorem

2018/08/24 by Tatsuji Kawai, Kawai, Tatsuji
Computer Science · Mathematics · #03B30 #03F55 #03F60 #26E40 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1808.08076

openalex publication_date 2018/08/24 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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 Π⁰₁ bars. We work in the context of constructive reverse mathematics.

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