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The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem
Journal of Symbolic Logic 72 (4):1379 - 1384 (2007)
Abstract
We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every pointwise continuous mapping of [0, 1] into R is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideasLinks
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Citations of this work
Sequences of real functions on [0, 1] in constructive reverse mathematics.Hannes Diener & Iris Loeb - 2009 - Annals of Pure and Applied Logic 157 (1):50-61.
Constructive notions of equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
The anti-Specker property, positivity, and total boundedness.Douglas Bridges & Hannes Diener - 2010 - Mathematical Logic Quarterly 56 (4):434-441.
Glueing continuous functions constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.
References found in this work
Equivalents of the (weak) fan theorem.Iris Loeb - 2005 - Annals of Pure and Applied Logic 132 (1):51-66.
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