Uniform Algebras in the Cantor and Baire Spaces
نویسنده
چکیده
For each pointclass Γ ⊆ P (2) define U [Γ] as the collection of all X ⊆ 2 such that the preimage f−1(X) belongs to Γ for each continuous f : 2 → 2. We study the properties of and possible relationships among the classes U [Γ], where Γ ranges over the σ-algebras (l), (m), the completely Ramsey sets, and the sets with the Baire property. We also prove some results about cardinal coefficients of U [Γ] for the general case of Marczewski-Burstin representable σ-algebras Γ. We finish by posing some unsolved problems.
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تاریخ انتشار 2009