Effective decomposition of $\sigma $-continuous Borel functions
Volume 224 / 2014
Fundamenta Mathematicae 224 (2014), 187-202
MSC: Primary 03E15; Secondary 26A21.
DOI: 10.4064/fm224-2-4
Abstract
We prove that if a $\varDelta^1_1$ function $f$ with $\varSigma^1_1$ domain $X$ is $\sigma$-continuous then one can find a $\varDelta^1_1$ covering $(A_n)_{n\in \omega}$ of $X$ such that $f_{\vert {A_n}}$ is continuous for all $n$. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.
