In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an -subset of X and contains a retract R so that is not homeomorphic to . This shows that Toruńczyk’s Factor Theorem fails in the Borel case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-1-3, author = {Tadeusz Dobrowolski and Witold Marciszewski}, title = {Failure of the Factor Theorem for Borel pre-Hilbert spaces}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {53-68}, zbl = {1019.57012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-1-3} }
Tadeusz Dobrowolski; Witold Marciszewski. Failure of the Factor Theorem for Borel pre-Hilbert spaces. Fundamenta Mathematicae, Tome 173 (2002) pp. 53-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-1-3/