On the closure of Baire classes under transfinite convergences

Tamás Mátrai. "On the closure of Baire classes under transfinite convergences." Fundamenta Mathematicae 183.2 (2004): 157-168. <http://eudml.org/doc/283214>.

@article{TamásMátrai2004,
abstract = {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.},
author = {Tamás Mátrai},
journal = {Fundamenta Mathematicae},
keywords = {transfinite convergence; Baire class; closure},
language = {eng},
number = {2},
pages = {157-168},
title = {On the closure of Baire classes under transfinite convergences},
url = {http://eudml.org/doc/283214},
volume = {183},
year = {2004},
}

TY - JOUR
AU - Tamás Mátrai
TI - On the closure of Baire classes under transfinite convergences
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 2
SP - 157
EP - 168
AB - 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.
LA - eng
KW - transfinite convergence; Baire class; closure
UR - http://eudml.org/doc/283214
ER -