We prove that there exists a model of $ZFC+``continuum=omega$₂'' in which every subset M of R of cardinality less than continuum is meager, and such that for every subset X of R of cardinality continuum there exists a continuous function f:R-->R with f[X]=[0,1].

In particular in this model there is no magic set, i.e., a subset M of R such that the equation f[M]=g[M] implies f=g for every continuous nowhere constant functions f,g:R-->R.

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Last modified October 20, 2001.