Pacific Journal of Mathematics

Continuity of monotone functions.

Mark Mandelkern

Article information

Source
Pacific J. Math., Volume 99, Number 2 (1982), 413-418.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102734025

Mathematical Reviews number (MathSciNet)
MR658070

Zentralblatt MATH identifier
0537.26001

Subjects
Primary: 26A48: Monotonic functions, generalizations
Secondary: 03F65: Other constructive mathematics [See also 03D45]

Citation

Mandelkern, Mark. Continuity of monotone functions. Pacific J. Math. 99 (1982), no. 2, 413--418. https://projecteuclid.org/euclid.pjm/1102734025


Export citation

References

  • [1] O. Aberth, Computable Analysis, McGraw-Hill, NewYork,1980.
  • [2] M.Beeson, Theunprovability in intuitionistic formal systems of the continuity of effective operations on the reals, J. Symbolic Logic, 41 (1976), 18-24.
  • [3] M.Beeson, Principles of continuous choice and continuity of functions in formal systems for constructive mathematics, Ann.Math. Logic, 12 (1977),249-322.
  • [4] E. Bishop, Foundations of Constructive Analysis, McGraw-Hill, NewYork,1967.
  • [5] L. E. J. Brouwer, Beweis, dass jede voile Funktion gleichmdssig ist, Proc. Akad. Amsterdam, 27 (1924), 189-194.
  • [6] G.S. Ceitin, Alhorithmic operators in constructive complete separable metric spaces, Dokl. Akad. Nauk SSSR, 128 (1959), 49-52 (Russian).
  • [7] A. Heyting, Intuitionism, an introduction, 3rded., North-Holland, Amsterdam, 1971.
  • [8] G.Kreisel,D.Lacombe andJ.R.Shoenfield,Fonctionnelles recursivement definissables et fonctionnellesrecursives, C.R.Acad. Sci. Paris Ser.A-B,245 (1957), 399-402.
  • [9] D.Lacombe, Remarques sur les operateurs recursifs et sur les fonctions recursives d'une variable reelle, C.R.Acad. Sci. Paris Ser.A-B,241 (1955), 1250-1252.
  • [10] M.Mandelkern, Connectivity of an interval, Proc. Amer. Matn. Soc, 54 (1976), 170-172.
  • [11] A. A. Markov, On the continuityof constructive functions,Uspehi Mat. Nauk.,~9 (1954), 226-230 (Russian).
  • [12] R. Mines and F. Richman, informal communication, August 1978.