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P. Holick´y, L. Zaj´ıˇcek, M. Zelen´y ) HA=H  = JDAHA B 5A?E

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P. Holick´ y, L. Zaj´ıˇ cek, M. Zelen´ y A remark on a theorem of Solecki

Comment.Math.Univ.Carolinae 46,1 (2005) 43-54.

Abstract: S. Solecki proved that ifF is a system of closed subsets of a complete separable metric space X, then each Suslin set S ⊂ X which cannot be covered by countably many members of F contains a

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δ set which cannot be covered by countably many members ofF. We show that the assumption of separability ofX cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that theσ-ideal generated by F is locally determined. Using Solecki’s arguments, our result can be used to reprove a Hurewicz type theorem due to Michalewski and Pol, and a nonseparable version of Feng’s theorem due to Chaber and Pol.

Keywords: Solecki’s theorem, Suslin set,σ-ideal AMS Subject Classification: 03E15, 28A05, 54H05

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