Failure of the Factor Theorem for Borel pre-Hilbert spaces

Tadeusz Dobrowolski, and Witold Marciszewski. "Failure of the Factor Theorem for Borel pre-Hilbert spaces." Fundamenta Mathematicae 175.1 (2002): 53-68. <http://eudml.org/doc/283245>.

@article{TadeuszDobrowolski2002,
abstract = {In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_\{σδσ\}$-subset of X and contains a retract R so that $R × E^\{ω\}$ is not homeomorphic to $E^\{ω\}$. This shows that Toruńczyk’s Factor Theorem fails in the Borel case.},
author = {Tadeusz Dobrowolski, Witold Marciszewski},
journal = {Fundamenta Mathematicae},
keywords = {factor theorem},
language = {eng},
number = {1},
pages = {53-68},
title = {Failure of the Factor Theorem for Borel pre-Hilbert spaces},
url = {http://eudml.org/doc/283245},
volume = {175},
year = {2002},
}

TY - JOUR
AU - Tadeusz Dobrowolski
AU - Witold Marciszewski
TI - Failure of the Factor Theorem for Borel pre-Hilbert spaces
JO - Fundamenta Mathematicae
PY - 2002
VL - 175
IS - 1
SP - 53
EP - 68
AB - In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_{σδσ}$-subset of X and contains a retract R so that $R × E^{ω}$ is not homeomorphic to $E^{ω}$. This shows that Toruńczyk’s Factor Theorem fails in the Borel case.
LA - eng
KW - factor theorem
UR - http://eudml.org/doc/283245
ER -