$F_{σ}$-mappings and the invariance of absolute Borel classes

Petr Holický; Jiří Spurný

F_{σ}

-mappings and the invariance of absolute Borel classes

Petr Holický ; Jiří Spurný

Fundamenta Mathematicae, Tome 184 (2004), p. 193-204 / Harvested from The Polish Digital Mathematics Library

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Résumé

It is proved that $F_{σ}$ -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 $F_{σ}$ -mapping f: X → 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 $F_{σ}$ -set $X_{\infty} \subset X$ satisfying $f (X_{\infty}) = Y$ .

Publié le : 2004-01-01

Zbl 1059.54025

EUDML-ID : urn:eudml:doc:282597

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Petr Holický; Jiří Spurný. $F_{σ}$-mappings and the invariance of absolute Borel classes. Fundamenta Mathematicae, Tome 184 (2004) pp. 193-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-3-1/