The σ-ideal of closed smooth sets does not have the covering property
Volume 150 / 1996
Fundamenta Mathematicae 150 (1996), 227-236 DOI: 10.4064/fm-150-3-227-236
We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.