Generalized projections of Borel and analytic sets

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Łódź Technical University, al. Politechniki 11, 90-924 Łódź, Poland

For a σ-ideal I of sets in a Polish space X and for A ⊆

X^{2}

, we consider the generalized projection (A) of A given by (A) = {x ∈ X: A_x ∉ I}, where

A_{x}

={y ∈ X: 〈x,y〉∈ A}. We study the behaviour of with respect to Borel and analytic sets in the case when I is a

\sum_{2}^{0}

-supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [

\sum_{1}^{1} (X^{2})] = \sum_{1}^{1} (X)

for a wide class of

\sum_{2}^{0}

-supported σ-ideals.

meager set, Effros Borel structure, analytic set, σ-ideal

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