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Bounded variation implies regulated: a constructive proof

  • Douglas Bridges (a1) and Ayan Mahalanobis
Abstract.
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.

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References
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[1]Bishop Errett. Foundations of constructive analysis, McGraw-Hill, New York, 1967.
[2]Bishop Errett and Bridges Douglas, Constructive analysis, Grundlehren der mathematische Wissenschaften, no. 279, Springer–Verlag, Heidelberg, 1985.
[3]Bridges Douglas, A constructive look at functions of bounded variation, Bulletin of the London Mathematical Society, vol. 32 (2000), no. 3, pp. 316324.
[4]Bridges Douglas and Mahalanobis Ayan, Constructive continuity of monotone functions, preprint; University of Canterbury, 1999.
[5]Bridges Douglas and Mahalanobis Ayan, Sequential continuity of functions in constructive analysis, Mathematical Logic Quarterly, vol. 46 (2000), no. 1, pp. 139143.
[6]Bridges Douglas and Richman Fred, Varieties of constructive mathematics, London Mathematical Society Lecture Notes, vol. 97, Cambridge University Press, 1987.
[7]Dieudonné J., Foundations of modern analysis, Academic Press, New York, 1960.
[8]Ishihara Hajime, Continuity and nondiscontinuity in constructive mathematics, this Journal, vol. 56 (1991), no. 4, pp. 13491354.
[9]Ishihara Hajime, A constructive version of banach's inverse mapping theorem, New Zealand Journal of Mathematics, vol. 23 (1995), pp. 7175.
[10]Troelstra A. S. and van Dalen D., Constructivism in mathematics: An introduction, North Holland, Amsterdam, 1988, two volumes.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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