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Continuity and nondiscontinuity in constructive mathematics

Published online by Cambridge University Press:  12 March 2014

Hajime Ishihara
Hajime Ishihara*
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima 730, Japan
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Abstract

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-Tseĭtin theorem.

Keywords

Sequentially continuoussequentially nondiscontinuousweak version of Markov's principleKreisel-Lacombe-Shoenfield-Tseĭtin theorem
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1349 - 1354
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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