Abstract
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.
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Bridges, D.S. Constructive notions of equicontinuity. Arch. Math. Logic 48, 437–448 (2009). https://doi.org/10.1007/s00153-009-0131-9
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DOI: https://doi.org/10.1007/s00153-009-0131-9