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  1. A Constructive Look at the Completeness of the Space $\Mathcal{D} (\Mathbb{R})$.Hajime Ishihara & Satoru Yoshida - 2002 - Journal of Symbolic Logic 67 (4):1511-1519.
    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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    A Constructive Look at the Completeness of the Space (ℝ).Hajime Ishihara & Satoru Yoshida - 2002 - Journal of Symbolic Logic 67 (4):1511-1519.
    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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    The Constructive Completion of the Space?Satoru Yoshida - 2005 - Mathematical Logic Quarterly 51 (1):77-82.
    We prove in the framework of Bishop's constructive mathematics that the sequential completion equation image of the space [MATHEMATICAL SCRIPT CAPITAL D] is filter-complete. Then it follows as a corollary that the filter-completeness of [MATHEMATICAL SCRIPT CAPITAL D] is equivalent to the principle BD-ℕ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that equation image is identical with the filter-completion which was (...)
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