On Projective Mappings

摘要: Let X,Y be Polish spaces, and let \(\mathcal{B}_k \) the σ-algebra generated by projective class \(L_{2k + 1} \). A mapping \(f:X \mapsto Y\) is called \(k\)-projective if \(f^{ - (E) \in \mathcal{B}_k for any Borel subset E ⊂ Y. The following theorem our main result: there exist a space \(\tilde X_s \), dense \(X_s two continuous mappings \(f_0 ,i:\tilde \to such that i) $${\text{i) }}f_0 {\text{|}}X_s = f \circ i|X_s ;$$