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Continuity properties 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, E-mail: ishihara@mis.hiroshima-u.ac.jp
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Abstract

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

Continuitysequential continuitysequential nondiscontinuityKreisel-Lacombe-Shoenfield-Tsejtin theoremconstructive
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 557 - 565
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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