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Sequences of real functions on [0, 1] in constructive reverse mathematics
TLDR
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
Compactness Under Constructive Scrutiny
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 thanExpand
The pseudocompactness of [0.1] is equivalent to the uniform continuity theorem
TLDR
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
Generalising compactness
Separating the Fan Theorem and Its Weakenings
TLDR
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
Constructive Reverse Mathematics
An introduction and overview of constructive reverse mathematics.
SEPARATING THE FAN THEOREM AND ITS WEAKENINGS
TLDR
We present a family of related Kripke models which separates all of the as yet identified fan theorems, corresponding to different continuity principles. Expand
Principles Weaker than BD-N
TLDR
We show that BD-N is a weak principle of constructive analysis, yet not provable in set theory alone under constructive logic. Expand
The anti-Specker property, positivity, and total boundedness
TLDR
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
Constructive reverse investigations into differential equations
TLDR
We study Picard's Theorem and Peano’s Theorem from a constructive reverse perspective. Expand
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