Skip to main content
Log in

Lipschitz mappings, contingents, and differentiability

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

The main purpose of the paper is to show that, for each real normed space Y of infinite dimension, each number L > 0, and each at most countable set Q ⊂ ℝ, there exists a Lipschitz mapping ƒ: ℝ → Y, with constant L, whose graph has a tangent everywhere, whereas ƒ is not differentiable at any point of Q.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schwartz L., Analyse mathématique. T. 1, Hermann, Paris (1967).

    Google Scholar 

  2. Bouligand G., Introduction à la géométrie infinitésimale directe, Librairie Vuibert, Paris (1932).

    Google Scholar 

  3. Federer H., Geometric Measure Theory, Springer-Verlag, Berlin (1968).

    Google Scholar 

  4. Flett T. M., Differential Analysis, Cambridge Univ. Press, London (1980).

    MATH  Google Scholar 

  5. Saks S., Theory of the Integral, Stechert, Warszawa; Lwów; New York (1937).

    Google Scholar 

  6. Turowska M., “A geometric condition for differentiability,” Tatra Mt. Math. Publ., 28, No. 2, 179–186 (2004).

    MATH  Google Scholar 

  7. Kottman C., “Subsets of the unit ball that separated by more than one,” Studia Math., 53, No. 1, 15–27 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 837–847, July–August, 2007.

Original Russian Text Copyright © 2007 Ponomarev S. and Turowska M.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ponomarev, S., Turowska, M. Lipschitz mappings, contingents, and differentiability. Sib Math J 48, 669–677 (2007). https://doi.org/10.1007/s11202-007-0069-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-007-0069-2

Keywords

Navigation