A constructive look at the completeness of the space (ℝ)
Hajime Ishihara, Satoru Yoshida · Journal of Symbolic Logic · 2002
Abstract We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space (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.