Strong Continuity Implies Uniform Sequential Continuity
Douglas Bridges, Hajime Ishihara, Peter Schuster and Luminita Vîta
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Abstract
Uniform sequential continuity, a property classically equivalent to uniform continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, in order to omit the word sequential from this result, it is necessary and sufficient to adopt a principle (BD-N) that is independent of Heyting arithmetic.
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