Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-08T11:27:01.540Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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