On the closure of Baire classes under transfinite convergences

• Autorzy: Tamás Mátrai
• Języki publikacji: EN

Abstrakty

EN

Let X be a Polish space and Y be a separable metric space. For a fixed ξ < ω₁, consider a family $f_{α}: X → Y~(α<ω₁)$ of Baire-ξ functions. Answering a question of Tomasz Natkaniec, we show that if for a function f: X → Y, the set ${α < ω₁: f_{α}(x) ≠ f(x)}$ is finite for every x ∈ X, then f itself is necessarily Baire-ξ. The proof is based on a characterization of $Σ⁰_{η}$ sets which can be interesting in its own right.

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 183
• Numer: 2
• Strony: 157-168

Daty

wydano

2004

Twórcy

autor

Tamás Mátrai

• Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm183-2-6