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

• Autorzy: Petr Holický , Jiří Spurný
• Języki publikacji: EN

Abstrakty

EN

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 $X_{∞} ⊂ X$ satisfying $f(X_{∞}) = Y$.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 3
• Strony: 193-204

Daty

wydano

2004

Twórcy

autor

Petr Holický

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

autor

Jiří Spurný

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm182-3-1