A constructive look at the completeness of the space $\mathcal{d} (\mathbb{r})$

Journal of Symbolic Logic 67 (4):1511-1519 (2002)
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Abstract

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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