Continuous images of big sets and additivity of
s_{0} under CPA_{prism}
by
Krzysztof Ciesielski,
and Janusz Pawlikowski
Real Anal. Exchange 29(2) (20032004), 755762.
We prove that the Covering Property Axiom CPA_{prism},
which holds in the iterated perfect set model, implies the following facts.

There exists a family G of uniformly continuous functions from R
to [0,1] such that G has cardinality \omega_{1} < \continuum and for every
subset S of R of cardinality
\continuum there exists a g in G with g[S]=[0,1].

The additivity of the Marczewski's ideal s_{0} is equal to \omega_{1} < \continuum.
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Last modified October 6, 2004.