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Uniform algebras in the cantor and baire spaces

Nowik A., Reardon P.

Journal of Applied Analysis

2008

Vol. 14, nr 2

227-238

For each pointclass Γ ⊆ P(2ω) define U[Γ] as the collection of all X⊆ 2ω such that the preimage f− 1(X) belongs to Γ for each continuous f : 2ω → 2ω. We study the properties of and possible rela-tionships 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.