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Strong continuity implies uniform sequential continuity |
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| Authors: | Douglas Bridges Hajime Ishihara Peter Schuster Luminiţa Vîţa |
| Institution: | 1. Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand 2. School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa, 923-12, Japan 3. Mathematisches Institut, Universit?t München, Theresienstra?e 39, 80333, München, Germany |
| 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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