On nowhere monotone functions
HTML articles powered by AMS MathViewer
- by Clifford E. Weil PDF
- Proc. Amer. Math. Soc. 56 (1976), 388-389 Request permission
Abstract:
The existence of everywhere differentiable but nowhere monotone functions is established using the Baire Category Theorem, and the relatively easy fact that there are nontrivial bounded derivatives with a dense set of zeros.References
- A. M. Bruckner and J. L. Leonard, Derivatives, Amer. Math. Monthly 73 (1966), no. 4, 24–56. MR 197632, DOI 10.2307/2313749
- Casper Goffman, Everywhere differentiable functions and the density topology, Proc. Amer. Math. Soc. 51 (1975), 250. MR 367124, DOI 10.1090/S0002-9939-1975-0367124-4 E. W. Hobson, Theory of functions of a real variable and the theory of Fourier series. Vol. 2, Dover, New York, 1958. MR 29, 1166.
- Y. Katznelson and Karl Stromberg, Everywhere differentiable, nowhere monotone, functions, Amer. Math. Monthly 81 (1974), 349–354. MR 335701, DOI 10.2307/2318996
- D. Pompeiu, Sur les fonctions dérivées, Math. Ann. 63 (1907), no. 3, 326–332 (French). MR 1511410, DOI 10.1007/BF01449201
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 388-389
- DOI: https://doi.org/10.1090/S0002-9939-1976-0396870-2
- MathSciNet review: 0396870