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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