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.
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