Continuous functions taking every value a given number of times
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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 $|F^{-1}(y)|=f(y)$.
💡 Research Summary
The paper addresses the following problem: given a prescribed cardinality function
(f:
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