On the Laczkovich-Komjáth property of sigma-ideals |
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Authors: | Marek Balcerzak Szymon G?a?b |
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Institution: | a Institute of Mathematics, ?ód? Technical University, ul. Wólczañska 215, 93-005 ?ód?, Poland b Mathematical Institute, Polish Academy of Sciences, ?niadeckich 8, 00-956 Warszawa, Poland |
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Abstract: | Komjáth in 1984 proved that, for each sequence (An) of analytic subsets of a Polish space X, if lim supn∈HAn is uncountable for every H∈ωN] then ?n∈GAn is uncountable for some G∈ωN]. This fact, by our definition, means that the σ-ideal X]?ω has property (LK). We prove that every σ-ideal generated by X/E has property (LK), for an equivalence relation E⊂X2 of type Fσ with uncountably many equivalence classes. We also show the parametric version of this result. Finally, the invariance of property (LK) with respect to various operations is studied. |
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Keywords: | 54H05 03E15 28A05 |
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