Notre Dame Journal of Formal Logic 47 (2):253-262 (2006)
Authors |
|
Abstract |
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
|
Keywords | compact metric spaces continuous functions uniform convergence reverse mathematics constructive mathematics |
Categories | (categorize this paper) |
DOI | 10.1305/ndjfl/1153858650 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
No references found.
Citations of this work BETA
Brouwer’s Fan Theorem as an Axiom and as a Contrast to Kleene’s Alternative.Wim Veldman - 2014 - Archive for Mathematical Logic 53 (5-6):621-693.
The Swap of Integral and Limit in Constructive Mathematics.Rudolf Taschner - 2010 - Mathematical Logic Quarterly 56 (5):533-540.
Similar books and articles
On the Role Played by the Work of Ulisse Dini on Implicit Function Theory in the Modern Differential Geometry Foundations: The Case of the Structure of a Differentiable Manifold, 1.Giuseppe Iurato - manuscript
The Fan Theorem and Unique Existence of Maxima.Josef Berger, Douglas Bridges & Peter Schuster - 2006 - Journal of Symbolic Logic 71 (2):713 - 720.
Query the Triple Loophole of the Proof of Gödel Incompleteness Theorem.FangWen Yuan - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:77-94.
Internationalisation of Information Services for Publishers' Open Access Policies: The DINI Multilingual Integration Layer.Frank Scholze - 2008 - Philosophy, Ethics, and Humanities in Medicine 3:19-.
Generalization of Scott's Formula for Retractions From Generalized Alexandroff's Cube.Jaros?aw Achinger - 1986 - Studia Logica 45 (3):281 - 292.
“The Connection Between Prudential Goodness and Moral Permissibility”, Journal of Social Philosophy 24 (1993): 105-28.Peter Vallentyne - 1993 - Journal of Social Philosophy 24:105-28.
Analytics
Added to PP index
2010-08-24
Total views
36 ( #281,567 of 2,404,057 )
Recent downloads (6 months)
5 ( #155,913 of 2,404,057 )
2010-08-24
Total views
36 ( #281,567 of 2,404,057 )
Recent downloads (6 months)
5 ( #155,913 of 2,404,057 )
How can I increase my downloads?
Downloads