$F_{\sigma}$-mappings and the invariance of absolute Borel classes
Volume 182 / 2004
Fundamenta Mathematicae 182 (2004), 193-204
MSC: 54H05, 54E40, 28A05.
DOI: 10.4064/fm182-3-1
Abstract
It is proved that $F_\sigma$-mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any $F_\sigma$-mapping $f:X\to Y$ of an absolute Suslin metric space $X$ onto an absolute Suslin metric space $Y$ becomes a piecewise perfect mapping when restricted to a suitable $F_\sigma$-set $X_\infty\subset X$ satisfying $f(X_\infty)=Y$.
