Abstract
This paper deals with continuity properties of functions f: X → Y between metric spaces X and Y within the framework of Bishop’s constructive mathematics. We concentrate on the situation when X is not complete. We investigate the relations between the properties of nondiscontinuity, sequential continuity, mapping Cauchy sequences to totally bounded sequences, and a certain boundedness condition.
The second author thanks the Japan Advanced Institute of Science and Technology and the JAIST Foundation for support of his stay in Japan from May 28 to August 2, 1998.
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Ishihara, H., Mines, R. (2001). Various Continuity Properties in Constructive Analysis. In: Schuster, P., Berger, U., Osswald, H. (eds) Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Synthese Library, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9757-9_9
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DOI: https://doi.org/10.1007/978-94-015-9757-9_9
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