Failure of the Factor Theorem for Borel pre-Hilbert spaces

Tadeusz Dobrowolski; Witold Marciszewski

Tadeusz Dobrowolski ; Witold Marciszewski

Fundamenta Mathematicae, Tome 173 (2002), p. 53-68 / Harvested from The Polish Digital Mathematics Library

Résumé

In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_{σ δ σ}$ -subset of X and contains a retract R so that $R \times E^{ω}$ is not homeomorphic to $E^{ω}$ . This shows that Toruńczyk’s Factor Theorem fails in the Borel case.

Publié le : 2002-01-01

Zbl 1019.57012

EUDML-ID : urn:eudml:doc:283245

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     year = {2002},
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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/