Geodesic
$F_{\sigma}$-mappings and the invariance of absolute Borel classes
Petr Holický 1   ; Jiří Spurný 1
1 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75, Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 182 (2004) no. 3, pp. 193-204 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $f(X_\infty)=Y$.
DOI : 10.4064/fm182-3-1
Keywords: proved sigma mappings preserve absolute borel classes which improves results hansell jayne rogers proof based sigma mapping absolute suslin metric space absolute suslin metric space becomes piecewise perfect mapping restricted suitable sigma set infty subset satisfying infty

Petr Holický  1   ; Jiří Spurný  1

1 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75, Praha 8, Czech Republic 
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Petr Holický; Jiří Spurný. $F_{\sigma}$-mappings and the invariance of absolute Borel classes. Fundamenta Mathematicae, Tome 182 (2004) no. 3, pp. 193-204. doi: 10.4064/fm182-3-1

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