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The pseudocompactness of \([0,1]\) is equivalent to the uniform continuity theorem. (English) Zbl 1132.03032
Summary: 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 \(\mathbb R\) is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideas.

MSC:
03F60 Constructive and recursive analysis
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