We give an overview of the role of equicontinuity of sequences of real-valued functions on [ 0 , 1 ] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics.Expand

The aim of this thesis is to understand the constructive scope of compactness. We show that it is possible to define, constructively, a meaningful notion of compactness in a more general setting than… Expand

We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every point wise continuous mapping of [0, 1] into ℝ is bounded.Expand

We present a family of related Kripke models which suffices to separate all of the as yet identified fan theorems.Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics.Expand

We present a family of related Kripke models which separates all of the as yet identified fan theorems, corresponding to different continuity principles.Expand

Working within Bishop-style constructive mathematics, we examine some of the consequences of the anti-Specker property, known to be equivalent to a version of Brouwer's fan theorem.Expand