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Failure of the Factor Theorem for Borel pre-Hilbert spaces

Tadeusz Dobrowolski, Witold Marciszewski (2002)

Fundamenta Mathematicae

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 × E ω is not homeomorphic to E ω . This shows that Toruńczyk’s Factor Theorem fails in the Borel case.

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