Continuity and nondiscontinuity in constructive mathematics

Journal of Symbolic Logic 56 (4):1349-1354 (1991)
The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem
Keywords Sequentially continuous   sequentially nondiscontinuous   weak version of Markov's principle   Kreisel-Lacombe-Shoenfield-Tseitin theorem
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DOI 10.2307/2275479
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References found in this work BETA
Constructively Complete Finite Sets.Mark Mandelkern - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):97-103.
Constructively Complete Finite Sets.Mark Mandelkern - 1988 - Mathematical Logic Quarterly 34 (2):97-103.

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Apartness Spaces as a Framework for Constructive Topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Uniform Continuity Properties of Preference Relations.Douglas S. Bridges - 2008 - Notre Dame Journal of Formal Logic 49 (1):97-106.
Weak-Operator Continuity and the Existence of Adjoints.Douglas Bridges & Luminita Dediu - 1999 - Mathematical Logic Quarterly 45 (2):203-206.

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