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We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering of X such that is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.
Gabriel Debs. "Effective decomposition of σ-continuous Borel functions." Fundamenta Mathematicae 224.2 (2014): 187-202. <http://eudml.org/doc/283173>.
@article{GabrielDebs2014, abstract = {We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering $(Aₙ)_\{n∈ω\}$ of X such that $f_\{|Aₙ\}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.}, author = {Gabriel Debs}, journal = {Fundamenta Mathematicae}, keywords = {-continuous; Borel functions; Wadge classes; product spaces}, language = {eng}, number = {2}, pages = {187-202}, title = {Effective decomposition of σ-continuous Borel functions}, url = {http://eudml.org/doc/283173}, volume = {224}, year = {2014}, }
TY - JOUR AU - Gabriel Debs TI - Effective decomposition of σ-continuous Borel functions JO - Fundamenta Mathematicae PY - 2014 VL - 224 IS - 2 SP - 187 EP - 202 AB - We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering $(Aₙ)_{n∈ω}$ of X such that $f_{|Aₙ}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki. LA - eng KW - -continuous; Borel functions; Wadge classes; product spaces UR - http://eudml.org/doc/283173 ER -