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

Archive for Mathematical Logic 58 (3-4):443-456 (2019)
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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 \ bars. We work in the context of constructive reverse mathematics.

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10.1007/s00153-018-0644-1

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References found in this work

Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.
Constructive Functional Analysis.D. S. Bridges & Peter Zahn - 1982 - Journal of Symbolic Logic 47 (3):703-705.

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