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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
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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

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References

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