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A generic property of globally smooth iterative roots. (English) Zbl 0838.39005
According to K. Simon [Proc. Am. Math. Soc. 106, No. 2, 455-463 (1989; Zbl 0675.28005); Acta Math. Hung. 55, No. 1/2, 133-134 (1990; Zbl 0709.26001)] and A. M. Blokh [Trans. Am. Math. Soc. 333, No. 2, 787-798 (1992; Zbl 0762.26002)] the set of all continuous self-mappings of \([0,1]\) which have a continuous iterative root of an order at least 2 is small in the sense of both Wiener measure and category.
In this paper a similar problem for some differentiable functions is studied from the topological point of view.
Reviewer: K.Baron (Katowice)

39B12 Iteration theory, iterative and composite equations
54C30 Real-valued functions in general topology
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems