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

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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 \(\varPi ^{0}_{1}\) bars. We work in the context of constructive reverse mathematics.

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Acknowledgements

I am grateful to Josef Berger and Makoto Fujiwara for useful discussions. I also thank Hajime Ishihara and Takako Nemoto for helpful comments. This work was carried out while the author was INdAM-COFUND-2012 fellow of Istituto Nazionale di Alta Matematica “F. Severi”(INdAM).

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  1. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Tatsuji Kawai

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  1. Tatsuji Kawai
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Kawai, T. A continuity principle equivalent to the monotone \(\Pi ^{0}_{1}\) fan theorem. Arch. Math. Logic 58, 443–456 (2019). https://doi.org/10.1007/s00153-018-0644-1

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  • DOI: https://doi.org/10.1007/s00153-018-0644-1

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