Perfect images of absolute Souslin and absolute Borel Tychonoff spaces

The perfect image of a Tychonoff space X that is a result of the Souslin operation applied to the resolvable sets of F. Hausdorff (called also H-sets) in any Tychonoff space containing X is of the same descriptive type. This answers a question of R.W. Hansell since, within Tychonoff spaces, it says that perfect mappings preserve scattered-K-analytic spaces. We get also a new proof of an analogous fact for tech-analytic spaces that was proved already by R.W. Hansell and S. Pan using another method. We show that various absolute Borel classes are preserved by perfect mappings generalizing a result of J.E. Jayne and C.A. Rogers who proved the same fact within metric spaces. In fact, more general absolute descriptive classes and their stability with respect to perfect mappings are investigated. (C) 2003 Published by Elsevier Science B.V.