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.
@article{bwmeta1.element.bwnjournal-article-fmv150i3p227bwm,
author = {Carlos Uzc\'ategui},
title = {The $\sigma$-ideal of closed smooth sets does not have the covering property},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {227-236},
zbl = {0865.03040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i3p227bwm}
}
Uzcátegui, Carlos. The σ-ideal of closed smooth sets does not have the covering property. Fundamenta Mathematicae, Tome 149 (1996) pp. 227-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i3p227bwm/
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