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- W1948431256 abstract "We prove in the framework of Bishop's constructive mathematics that the sequential completion documentclass{article}usepackage{amssymb}pagestyle{empty}begin{document}$ tilde {cal D} $end{document}(ℝ) of the space 𝒟(ℝ) is filter-complete. Then it follows as a corollary that the filter-completeness of 𝒟(ℝ) is equivalent to the principle BD-ℕ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that documentclass{article}usepackage{amssymb}pagestyle{empty}begin{document}$ tilde {cal D} $end{document}(ℝ) is identical with the filter-completion which was provided by Bishop. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)" @default.
- W1948431256 created "2016-06-24" @default.
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- W1948431256 date "2005-01-01" @default.
- W1948431256 modified "2023-10-16" @default.
- W1948431256 title "The constructive completion of the space ?(?)" @default.
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- W1948431256 doi "https://doi.org/10.1002/malq.200310128" @default.
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