Annals of Pure and Applied Logic 157 (1):50-61 (2009)
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| Abstract |
We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles
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| DOI | 10.1016/j.apal.2008.09.018 |
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References found in this work BETA
The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem.Douglas Bridges & Hannes Diener - 2007 - Journal of Symbolic Logic 72 (4):1379 - 1384.
Compactness Under Constructive Scrutiny.Hajime Ishihara & Peter Schuster - 2004 - Mathematical Logic Quarterly 50 (6):540-550.
A Bizarre Property Equivalent To The -Fan Theorem.Josef Berger & Douglas Bridges - 2006 - Logic Journal of the IGPL 14 (6):867-871.
Elements of Intuitionistic Analysis II the Stone‐Weierstrass Theorem and Ascoli's Theorem.H. de Swart - 1976 - Mathematical Logic Quarterly 22 (1):501-508.
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Citations of this work BETA
Constructive Notions of Equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Toward a Clarity of the Extreme Value Theorem.Karin U. Katz, Mikhail G. Katz & Taras Kudryk - 2014 - Logica Universalis 8 (2):193-214.
Separating the Fan Theorem and its Weakenings.Robert S. Lubarsky & Hannes Diener - 2014 - Journal of Symbolic Logic 79 (3):792-813.
Glueing Continuous Functions Constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.
View all 12 citations / Add more citations
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