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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
##### Keywords:
constructive mathematics
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##### References:
 [1] DOI: 10.1007/11494645_3 [2] The Journal of Universal Computer Science 11 pp 1878– (2005) [3] Basic topology (1983) [4] Notes on constructive set theory (2001) [5] DOI: 10.1016/j.apal.2004.07.002 · Zbl 1060.03081 [6] DOI: 10.1007/11780342_4 [7] Techniques of constructive analysis (2006) · Zbl 1107.03065 [8] DOI: 10.1112/blms/8.2.179 · Zbl 0333.02028 [9] Constructive analysis 279 (1985) · Zbl 0656.03042 [10] A fan-theoretic equivalent of the antithesis of Specker’s theorem (2006) [11] Varieties of constructive mathematics 97 (1987)
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