Uncountable intersections of open sets under CPAprism
by
Krzysztof Ciesielski,
and Janusz Pawlikowski
Proc. Amer. Math. Soc. 132(11) (2004), 3379-3385.
We prove that the Covering Property Axiom CPAprism,
which holds in the iterated perfect set model, implies the following facts.
-
If G is an intersection of \omega1-many open sets
of a Polish space and G has cardinality continuum then G contains a perfect set.
-
There exists a subset G of the Cantor set
which is an intersection of \omega1-many open sets
but is not a union of \omega1-many closed sets.
The example from the second fact refutes a conjecture of Brendle, Larson, and Todorcevic.\omega1<\continuum.
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Last modified July 20, 2004.