Abstract
Uniform sequential continuity, a property classically equivalent to sequential 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, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.
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Bridges, D., Ishihara, H., Schuster, P. et al. Strong continuity implies uniform sequential continuity. Arch. Math. Logic 44, 887–895 (2005). https://doi.org/10.1007/s00153-005-0291-1
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DOI: https://doi.org/10.1007/s00153-005-0291-1