2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136769We give necessary and sufficient conditions on a function $f:[0,1]\to {0,1,2,...,ω,\continuum}$ under which there exists a continuous function $F:[0,1]\to [0,1]$ such that for every $y\in[0,1]$ we have $|F^{-1}(y)|=f(y)$.16 pages, 2 figuresLogicGeneral Topology26A21; 03E15text