Translator Disclaimer
December 2007 The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem
Douglas Bridges, Hannes Diener
J. Symbolic Logic 72(4): 1379-1384 (December 2007). DOI: 10.2178/jsl/1203350793

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.

Citation

Download Citation

Douglas Bridges. Hannes Diener. "The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem." J. Symbolic Logic 72 (4) 1379 - 1384, December 2007. https://doi.org/10.2178/jsl/1203350793

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1132.03032
MathSciNet: MR2371212
Digital Object Identifier: 10.2178/jsl/1203350793

Rights: Copyright © 2007 Association for Symbolic Logic

JOURNAL ARTICLE
6 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.72 • No. 4 • December 2007
Back to Top