Constructive notions of equicontinuity

Archive for Mathematical Logic 48 (5):437-448 (2009)

In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N
Keywords Constructive  Reverse mathematics  Anti-specker property  Pseudobounded  Fan theorem
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DOI 10.1007/s00153-009-0131-9
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References found in this work BETA

Constructive Set Theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Equivalents of the (Weak) Fan Theorem.Iris Loeb - 2005 - Annals of Pure and Applied Logic 132 (1):51-66.
Continuity Properties in Constructive Mathematics.Hajime Ishihara - 1992 - Journal of Symbolic Logic 57 (2):557-565.

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On the Constructive Notion of Closure Maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.

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