Abstract
AbstractWe prove in the framework of Bishop's constructive mathematics that the sequential completion \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \tilde {\cal D} $\end{document}(â) of the space đ(â) is filterâcomplete. Then it follows as a corollary that the filterâcompleteness of đ(â) is equivalent to the principle BDââ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \tilde {\cal D} $\end{document}(â) is identical with the filterâcompletion which was provided by Bishop. (© 2004 WILEYâVCH Verlag GmbH & Co. KGaA, Weinheim)
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