A constructive look at the completeness of the space (ℝ)

Journal of Symbolic Logic 67 (4):1511-1519 (2002)
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We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism



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Citations of this work

Constructive notions of equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Intuitionistic notions of boundedness in ℕ.Fred Richman - 2009 - Mathematical Logic Quarterly 55 (1):31-36.
Reflections on function spaces.Douglas S. Bridges - 2012 - Annals of Pure and Applied Logic 163 (2):101-110.
Continuity properties of preference relations.Marian A. Baroni & Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (5):454-459.

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References found in this work

Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.
Constructive Functional Analysis.D. S. Bridges & Peter Zahn - 1982 - Journal of Symbolic Logic 47 (3):703-705.

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