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Generalized projections of Borel and analytic sets

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Balcerzak M.

Colloquium Mathematicum

1996

tom 71

nr 1

47-53

For a σ-ideal I of sets in a Polish space X and for A ⊆ $X^2$, we consider the generalized projection 𝛷(A) of A given by 𝛷(A) = {x ∈ X: A_x ∉ I}, where $A_x$ ={y ∈ X: 〈x,y〉∈ A}. We study the behaviour of 𝛷 with respect to Borel and analytic sets in the case when I is a $∑_{2}^{0}$-supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that 𝛷 [$∑_{1}^{1}(X^2)]=∑_{1}^{1}(X)$ for a wide class of $∑_{2}^{0}$-supported σ-ideals.

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1 Colloquium Mathematicum

1 Balcerzak M.

1 1996

Wyniki wyszukiwania

Generalized projections of Borel and analytic sets