Effective decomposition of σ-continuous Borel functions

Gabriel Debs

Gabriel Debs

Fundamenta Mathematicae, Tome 227 (2014), p. 187-202 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering ${(A ₙ)}_{n \in ω}$ of X such that $f_{| A ₙ}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

Publié le : 2014-01-01

Zbl 1338.03091

EUDML-ID : urn:eudml:doc:283173

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     author = {Gabriel Debs},
     title = {Effective decomposition of $\sigma$-continuous Borel functions},
     journal = {Fundamenta Mathematicae},
     volume = {227},
     year = {2014},
     pages = {187-202},
     zbl = {1338.03091},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-4}
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Gabriel Debs. Effective decomposition of σ-continuous Borel functions. Fundamenta Mathematicae, Tome 227 (2014) pp. 187-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-4/