Constructive notions of equicontinuity

Constructive notions of equicontinuity

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 sequ...

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Veröffentlicht in:Archive for mathematical logic 2009-06, Vol.48 (5), p.437-448
1. Verfasser: Bridges, Douglas S.
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Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theorems
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description 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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subjects Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theorems
title Constructive notions of equicontinuity
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