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Open AccessArticle10.4064/fm-150-3-227-236

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

Carlos Uzcátegui-1996-01-01-Fundamenta Mathematicae
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TL;DRAbstract

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

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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

Keywords

MathematicsIdeal (ethics)Equivalence relationProperty (philosophy)Equivalence (formal languages)Pure mathematicsClosed setDiscrete mathematics

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