3 citations · 3 across the 12 of their papers we have counts for
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Axiomatic Justification in Constructive Morse Set Theory
Douglas S. Bridges
Working within Constructive Morse Set Theory (CMST), we introduce axioms for a new notion, jst Pp, intended to capture what it means for P to prove, or justify, p under the BHK int…
Monotone convergence theorems equivalent to Markov's principle
Douglas S. Bridges
The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop-style constructive mathematics…
On Constructive Connectedness Properties
Douglas S. Bridges
We plug two gaps in the constructive proof of Theorem 1 (respectively, Theorem 2) in <cite>dsb</cite>, showing that the property of C-connectedness (respectively, O-connectedness)…
Metric Double Complements of Convex Sets
Douglas S. Bridges
In constructive mathematics the metric complement of a subset S of a metric space X is the set -S of points in X that are bounded away from S. In this note we discuss, within Bisho…
Affine Hulls and Simplices: a Constructive Analysis
Douglas S. Bridges
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, w…
On the Constructive Theory of Jordan Curves
Douglas S. Bridges
Using a definition of Jordan curve similar to that of Dieudonné, we prove that our notion is equivalent to that used by Berg et al. in their constructive proof of the Jordan Curve…
Improving Cauchy's Theorem in Constructive Analysis
Douglas S. Bridges
In his constructive development of complex analysis, Errett Bishop used restrictive notions of homotopy and simple connectedness. Working in Bishop-style constructive mathematics,…
Constructive aspects of Riemann's permutation theorem for series
J. Berger, D. Bridges, H. Diener +1
The notions of permutable and weak-permutable convergence of a series of real numbers are introduced. Classically, these two notions are equivalent, and,…