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

Petr Holický, and Jiří Spurný. "$F_{σ}$-mappings and the invariance of absolute Borel classes." Fundamenta Mathematicae 182.3 (2004): 193-204. <http://eudml.org/doc/282597>.

@article{PetrHolický2004,
abstract = {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 $f(X_\{∞\}) = Y$.},
author = {Petr Holický, Jiří Spurný},
journal = {Fundamenta Mathematicae},
keywords = {metrizable space; Suslin set; absolute Suslin space; piecewise perfect mapping; Borel hierarchy; Borel class},
language = {eng},
number = {3},
pages = {193-204},
title = {$F_\{σ\}$-mappings and the invariance of absolute Borel classes},
url = {http://eudml.org/doc/282597},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Petr Holický
AU - Jiří Spurný
TI - $F_{σ}$-mappings and the invariance of absolute Borel classes
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 3
SP - 193
EP - 204
AB - 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 $f(X_{∞}) = Y$.
LA - eng
KW - metrizable space; Suslin set; absolute Suslin space; piecewise perfect mapping; Borel hierarchy; Borel class
UR - http://eudml.org/doc/282597
ER -