On the closure of Baire classes under transfinite convergences

Tamás Mátrai

Tamás Mátrai

Fundamenta Mathematicae, Tome 184 (2004), p. 157-168 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be a Polish space and Y be a separable metric space. For a fixed ξ < ω₁, consider a family $f_{α} : X \to Y (α < ω ₁)$ of Baire-ξ functions. Answering a question of Tomasz Natkaniec, we show that if for a function f: X → Y, the set $α < ω ₁ : f_{α} (x) \neq f (x)$ is finite for every x ∈ X, then f itself is necessarily Baire-ξ. The proof is based on a characterization of $Σ ⁰_{η}$ sets which can be interesting in its own right.

Publié le : 2004-01-01

Zbl 1071.26004

EUDML-ID : urn:eudml:doc:283214

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     title = {On the closure of Baire classes under transfinite convergences},
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     volume = {184},
     year = {2004},
     pages = {157-168},
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     language = {en},
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Tamás Mátrai. On the closure of Baire classes under transfinite convergences. Fundamenta Mathematicae, Tome 184 (2004) pp. 157-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-2-6/