Abstract
The principal results of this paper are: in constructive mathematics (1) the theorem “Mappings from a complete metric space into a metric space are sequentially continuous” can be proved using a disjunctive form of Church's thesis only, and (2) the theorem “Every open cover of a complete separable metric space has an enumerable subcover” can be proved using the Extended Church's Thesis only; Markov's principle is not needed.
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