  A set of reals is nowhere dense iff its closure under limits contains no open sets. A set of reals is meager iff it is the countable union of nowhere dense sets. Finally, a set of reals A has the property of Baire iff it is “almost open” in the sense that there is an open set O such that the region where O and A do not overlap (that is, the symmetric difference (O − A) ∪ (A − O)) is meager. It is straightforward to show that all Borel sets have the property of Baire. Do all of the projective sets have the property of Baire? 