Failure of the Factor Theorem for Borel pre-Hilbert spaces
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 53-68
MSC: 57N17, 46C05.
DOI: 10.4064/fm175-1-3
Abstract
In every infinite-dimensional Fréchet space $X$, we construct a linear subspace $E$ such that $E$ is an $F_{\sigma \delta \sigma }$-subset of $X$ and contains a retract $R$ so that $R\times E^\omega $ is not homeomorphic to $E^\omega $. This shows that Toruńczyk's Factor Theorem fails in the Borel case.
