Abstract
We give necessary and sufficient conditions for a function f: [0, 1] → {1,2,...,w, c} under which there exists a continuous function F: [0, 1] → [0, 1] such that for every y ɛ [0, 1], |F −1 (y)| = f(y).
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Kwiatkowska, A. Continuous functions taking every value a given number of times. Acta Math Hung 121, 229–242 (2008). https://doi.org/10.1007/s10474-008-7042-9
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DOI: https://doi.org/10.1007/s10474-008-7042-9