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

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 3, page 227-236
- ISSN: 0016-2736

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topUzcátegui, Carlos. "The σ-ideal of closed smooth sets does not have the covering property." Fundamenta Mathematicae 150.3 (1996): 227-236. <http://eudml.org/doc/212173>.

@article{Uzcátegui1996,

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.},

author = {Uzcátegui, Carlos},

journal = {Fundamenta Mathematicae},

keywords = {closed smooth sets; transversals; -ideal of compact sets; Polish space; covering property; analytic set; Borel sets; smooth Borel equivalence relation; Borel basis},

language = {eng},

number = {3},

pages = {227-236},

title = {The σ-ideal of closed smooth sets does not have the covering property},

url = {http://eudml.org/doc/212173},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Uzcátegui, Carlos

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

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 3

SP - 227

EP - 236

AB - 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.

LA - eng

KW - closed smooth sets; transversals; -ideal of compact sets; Polish space; covering property; analytic set; Borel sets; smooth Borel equivalence relation; Borel basis

UR - http://eudml.org/doc/212173

ER -

## References

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