Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-20T16:34:26.492Z Has data issue: false hasContentIssue false
  • English
  • Français

Functions with finite intersections with analytic functions

Published online by Cambridge University Press:  14 November 2011

Zoltán Buczolich
Zoltán Buczolich
Affiliation:
Department of Analysis, Eötvös Loránd University, Múzeum krt.6–8, H–1088 Budapest, Hungary
Get access Rights & Permissions [Opens in a new window]

Synopsis

We prove that for every dense Gδ set H, there exists a continuous function f, such that f intersects every analytic function in finitely many points and f is infinitely differentiable exactly at the points of H. This answers a problem of S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss. They proved a result which implies that every continuous function with finite intersections with analytic functions is infinitely differentiable at the points of a dense Gδ set.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 271 - 275
Copyright
Copyright © Royal Society of Edinburgh 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Agronsky, S., Bruckner, A. M., Laczkovich, M. and Preiss, D.. Convexity conditions and intersections with smooth functions. Trans. Amer. Math. Soc. 289 (1985), 659–677.CrossRefGoogle Scholar
2Cartan, H.. Collected Works (Berlin: Springer, 1979).Google Scholar
3Sierpinski, W.. Sur une propriété des ensembles F o linéaires. Fund. Math. 14 (1929), 216–220.CrossRefGoogle Scholar
4Zahorski, Z.. Sur l'ensemble des points singuliers d'une fonction d'une variable réelle admittant les dérivés de tous les ordres. Fund. Math. 34 (1947), 183–245.CrossRefGoogle Scholar