3 citations · 3 across the 12 of their papers we have counts for
12 papers
Locatedness, Convexity, and Measurability in
Douglas S Bridges
We prove, within Bishop's constructive framework, stronger forms of two theorems in the author's 1988 paper about the locatedness of certain Lebesgue measurable complemented sets i…
Notes on q-normed Spaces in Constructive Analysis
Douglas S. Bridges
What we call q-normed (linear) spaces were introduced (under the name pseudonormed spaces) into constructive analysis by D.L. Johns as a means of handling spaces, such as L-infinit…
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…
Constructive Notes on Locally Convex Spaces
Douglas S. Bridges
We give a detailed, corrected presentation of some fundamentals of the constructive theory of locally convex spaces that appear without proofs in <cite>BVtech</cite>. This suffices…
A Constructive Version of Ekeland's Variational Principle
Douglas S. Bridges
Building on preliminary results about lower sections of real-valued functions on a metric space, we provide a constructive counterpart of Ekeland's theorem on the approximate optim…
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,…