Continuity properties in constructive mathematics

Journal of Symbolic Logic 57 (2):557-565 (1992)
The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism
Keywords Continuity   sequential continuity   sequential nondiscontinuity   Kreisel-Lacombe-Shoenfield-Tsejtin theorem   constructive
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