Archive for Mathematical Logic

, Volume 58, Issue 3–4, pp 443–456 | Cite as

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

  • Tatsuji KawaiEmail author


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.


Constructive reverse mathematics Fan theorem Strongly continuous function Complete separable metric space 

Mathematics Subject Classification

03F60 03F55 03B30 26E40 


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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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Japan Advanced Institute of Science and TechnologyIshikawaJapan

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