Archive for Mathematical Logic

, Volume 48, Issue 5, pp 437–448

# 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

03F60

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