Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 47, Number 2 (2006), 253-262.
Classifying Dini's Theorem
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.
Notre Dame J. Formal Logic, Volume 47, Number 2 (2006), 253-262.
First available in Project Euclid: 25 July 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03F60: Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]
Secondary: 26E40: Constructive real analysis [See also 03F60] 54E45: Compact (locally compact) metric spaces
Berger, Josef; Schuster, Peter. Classifying Dini's Theorem. Notre Dame J. Formal Logic 47 (2006), no. 2, 253--262. doi:10.1305/ndjfl/1153858650. https://projecteuclid.org/euclid.ndjfl/1153858650