Linear extensions of some Baire-one functions (Q1692350)

Let \(\mathcal P_0(X)\) be the family of all real functions on \(X\) such that there is a sequence of closed \(G_\delta\) sets \(X_i\) such that \(X=\bigcup_{i=1}^\infty X_i\) and the restrictions \(f\restriction X_i\) are continuous, and let \(\mathcal P_0^b(X)\) be the bounded functions in \(\mathcal P_0(X)\). The main result of the paper is that if \(X\) is a normal space, \(A\) is a closed \(G_\delta\) set in \(X\) and \(f\in \mathcal P_0(A)\) then there is a linear extension of \(f\) such that its restriction to \(\mathcal P_0^b(A)\) is an isometry into \(\mathcal P_0^b(X)\).