10 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…