Uncountable intersections of open sets under CPA_{jlcmg}
Krzysztof Ciesielski, Janusz M. Pawlikowski · Proceedings of the American Mathematical Society · 2004
We prove that the Covering Property Axiom CPA p r i s m _{\mathrm {prism}} , which holds in the iterated perfect set model, implies the following facts. If G G is an intersection of ω 1 \omega _1 -many open sets of a Polish space and G G has cardinality continuum, then G G contains a perfect set. There exists a subset G G of the Cantor set which is an intersection of ω 1 \omega _1 -many open sets but is not a union of ω 1 \omega _1 -many closed sets. The example from the second fact refutes a conjecture of Brendle, Larson, and Todorcevic.