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Title

The σ-ideal of closed smooth sets does not have the covering property

Authors 1

Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, Venezuela

Abstract

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.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm150/fm15033.pdf

Fundamenta Mathematicae
1996/150/3
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Pages:
227-236
Main language of publication
English
Received
1994-12-21
Published
1996
Exact and natural sciences