Real Analysis Exchange

Most CĮ Functions Are Nowhere Gevrey Differentiable of Any Order

F. S. Cater

Full-text: Open access


We define a complete metric on $C^\infty$, and find that most functions in $C^\infty$ are nowhere Gevrey differentiable of any order. For any $s > 1$ we prove there exists an everywhere Gevrey differentiable function of order $s$ that is nowhere Gevrey differentiable of any order less than $s$.

Article information

Real Anal. Exchange, Volume 27, Number 1 (2001), 77-80.

First available in Project Euclid: 6 June 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26A99: None of the above, but in this section

Gevrey differentiable complete metric


Cater, F. S. Most C Į Functions Are Nowhere Gevrey Differentiable of Any Order. Real Anal. Exchange 27 (2001), no. 1, 77--80.

Export citation


  • Soon-Yeong Chung, A Gevrey differentiable function which is nowhere analytic (to appear).
  • J. Dugundji, Topology, Allyn & Bacon, Boston, 1966, 301–302.
  • S. S. Kim and K. H. Kwon, Smooth $(C^\infty)$ but nowhere analytic functions, Amer. Math. Monthly, 107 (2000), 264–266.