Archive for Mathematical Logic

, Volume 48, Issue 5, pp 437–448 | Cite as

Constructive notions of equicontinuity

Article

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.

Keywords

Constructive Reverse mathematics Anti-specker property Pseudobounded Fan theorem 

Mathematics Subject Classification (2000)

03F60 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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