Journal of Symbolic Logic

The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem

Douglas Bridges and Hannes Diener

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Symbolic Logic, Volume 72, Issue 4 (2007), 1379-1384.

First available in Project Euclid: 18 February 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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.

Export citation