Open Access
2006 Classifying Dini's Theorem
Josef Berger, Peter Schuster
Notre Dame J. Formal Logic 47(2): 253-262 (2006). DOI: 10.1305/ndjfl/1153858650


Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, in the original classical setting of reverse mathematics started by Friedman and Simpson.


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Josef Berger. Peter Schuster. "Classifying Dini's Theorem." Notre Dame J. Formal Logic 47 (2) 253 - 262, 2006.


Published: 2006
First available in Project Euclid: 25 July 2006

zbMATH: 1156.03055
MathSciNet: MR2240623
Digital Object Identifier: 10.1305/ndjfl/1153858650

Primary: 03F60
Secondary: 26E40 , 54E45

Keywords: compact metric spaces , Constructive mathematics , continuous functions , reverse mathematics , Uniform convergence

Rights: Copyright © 2006 University of Notre Dame

Vol.47 • No. 2 • 2006
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