Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 72, Issue 4 (2007), 1379-1384.
The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem
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.
J. Symbolic Logic, Volume 72, Issue 4 (2007), 1379-1384.
First available in Project Euclid: 18 February 2008
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Bridges, Douglas; Diener, Hannes. The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem. J. Symbolic Logic 72 (2007), no. 4, 1379--1384. doi:10.2178/jsl/1203350793. https://projecteuclid.org/euclid.jsl/1203350793