Compact covering mappings on a Borel space

We prove that if N-1(L) < N-1 (N-2(L) < N-1), then any compact covering mapping from a space Delta (1)(1) onto a space Sigma (0)(3) (Sigma (0)(4)) is inductively perfect. We conjecture that if "For All alpha is an element of omega (omega), N-1(L(alpha)) < N1", the same result holds for any mapping between two Borel spaces. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.