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The pseudocompactness of [0.1] is equivalent to the uniform continuity theorem
Published online by Cambridge University Press: 12 March 2014
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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- Copyright © Association for Symbolic Logic 2007
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