Perfect images of absolute Souslin and absolute Borel Tychonoff spaces
One of the main results of the paper says that perfect images of Tychonoff scattered-\(K\)-analytic spaces are scattered-\(K\)-analytic if they are Tychonoff. This answers a question of \textit{R.~W. Hansell} [Serdica Math.~J.~27, 1-66 (2001; Zbl 0982.46012)] who introduced scattered-\(K\)-analytic spaces in the context of nonseparable Banach spaces. At the same time the authors get an alternative simple proof of the result of R.~W. Hansel and S.~Pan saying that Čech-analytic spaces are preserved by perfect mappings. The authors also generalize a~result of J.~Saint-Raymond and a~result of J.~E. Jayne and C.~A. Rogers on stability of various absolute Borel classes with respect to perfect mappings to the nonmetrizable case. In fact, more general absolute descriptive classes and their stability with respect to perfect mappings are investigated.
scientific article; zbMATH DE number 1955999
scientific article