Continuous functions taking every value a given number of times

Details Continuous functions taking every value a given number of times Continuous functions taking every value a given number of times

2007-08-26

arxiv.org/abs/0708.3608v1

Mathematics

Logic

16 pages, 2 figures

Scientific paper

We give necessary and sufficient conditions on a function $f:[0,1]\to
{0,1,2,...,\omega,\continuum}$ under which there exists a continuous function
$F:[0,1]\to [0,1]$ such that for every $y\in[0,1]$ we have $|F^{-1}(y)|=f(y)$.

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