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Homeomorphisms of an interval and smoothness of a function. (English. Russian original) Zbl 0637.26006
Math. Notes 40, 713-719 (1986); translation from Mat. Zametki 40, No. 3, 364-373 (1986).
Conditions are given under which for a function $$f\in C(I)$$ a homeomorphism $$h: I\to I$$ exists such that the superposition $$f\circ h$$ belongs to $$C^ p(I)\quad (1\leq p<\infty).$$ Analogical question for the validity of $$f\circ h\in C^{\infty}(I)$$ is also discussed.
Reviewer: A.Neubrunnová

##### MSC:
 26A99 Functions of one variable 26E10 $$C^\infty$$-functions, quasi-analytic functions
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##### References:
 [1] A. M. Bruckner and C. Goffman, ?Differentiability through changes of variables,? Proc. Am. Math. Soc.,61, 235-341 (1976). [2] I. P. Natanson, Theory of Functions of Real Variables, Ungar. · Zbl 0064.29102 [3] P. S. Aleksandrov, Introduction to the Theory of Sets and General Topology [in Russian], Nauka, Moscow (1977).
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