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Bounded variation implies regulated: a constructive proof

Published online by Cambridge University Press:  12 March 2014

Douglas Bridges  and
Ayan Mahalanobis
Douglas Bridges
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand, E-Mail: d.bridges@math.canterbury.ac.nz
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Abstract.

It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1695 - 1700
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Bishop, Errett. Foundations of constructive analysis, McGraw-Hill, New York, 1967.Google Scholar
[2]Bishop, Errett and Bridges, Douglas, Constructive analysis, Grundlehren der mathematische Wissenschaften, no. 279, Springer–Verlag, Heidelberg, 1985.CrossRefGoogle Scholar
[3]Bridges, Douglas, A constructive look at functions of bounded variation, Bulletin of the London Mathematical Society, vol. 32 (2000), no. 3, pp. 316–324.CrossRefGoogle Scholar
[4]Bridges, Douglas and Mahalanobis, Ayan, Constructive continuity of monotone functions, preprint; University of Canterbury, 1999.Google Scholar
[5]Bridges, Douglas and Mahalanobis, Ayan, Sequential continuity of functions in constructive analysis, Mathematical Logic Quarterly, vol. 46 (2000), no. 1, pp. 139–143.3.0.CO;2-B>CrossRefGoogle Scholar
[6]Bridges, Douglas and Richman, Fred, Varieties of constructive mathematics, London Mathematical Society Lecture Notes, vol. 97, Cambridge University Press, 1987.CrossRefGoogle Scholar
[7]Dieudonné, J., Foundations of modern analysis, Academic Press, New York, 1960.Google Scholar
[8]Ishihara, Hajime, Continuity and nondiscontinuity in constructive mathematics, this Journal, vol. 56 (1991), no. 4, pp. 1349–1354.Google Scholar
[9]Ishihara, Hajime, A constructive version of banach's inverse mapping theorem, New Zealand Journal of Mathematics, vol. 23 (1995), pp. 71–75.Google Scholar
[10]Troelstra, A. S. and van Dalen, D., Constructivism in mathematics: An introduction, North Holland, Amsterdam, 1988, two volumes.Google Scholar