The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem

Journal of Symbolic Logic 72 (4):1379 - 1384 (2007)
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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 ideas

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Citations of this work

Constructive mathematics.Douglas Bridges - 2008 - Stanford Encyclopedia of Philosophy.
Constructive notions of equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Glueing continuous functions constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.

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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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