Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T07:47:02.350Z Has data issue: false hasContentIssue false
  • English
  • Français

Most Infinitely Differentiable Functions are Nowhere Analytic

Published online by Cambridge University Press:  20 November 2018

R. B. Darst
R. B. Darst*
Affiliation:
Colorado State University, Fort Collins, Colorado
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We define a natural metric, d, on the space, C∞,, of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, and show that C∞, is complete with respect to this metric. Then we show that the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C∞,.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 597 - 598
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Katznelson, Y., An introduction to harmonic analysis, Wiley, New York, 1968.Google Scholar
2. Rudin, W., Principles of mathematical analysis, 2nd ed., McGraw-Hill, New York, 1964.Google Scholar
3. May, L. E., On C∞ functions analytic on sets of small measure, Canad. Math. Bull. 12 (1969), 25–30.Google Scholar