Geodesic
Failure of the Factor Theorem for Borel pre-Hilbert spaces
Tadeusz Dobrowolski 1   ; Witold Marciszewski 2
1 Department of Mathematics Pittsburg State University Pittsburg, KS 66762, U.S.A. and Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland and Division of Mathematics and Computer Science Faculty of Sciences Vrije Universiteit De Boelelaan 1081a 1081 HV Amsterdam, The Netherlands
Fundamenta Mathematicae, Tome 175 (2002) no. 1, pp. 53-68 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm175-1-3
Keywords: every infinite dimensional chet space construct linear subspace sigma delta sigma subset contains retract times omega homeomorphic omega shows toru czyks factor theorem fails borel

Tadeusz Dobrowolski  1   ; Witold Marciszewski  2

1 Department of Mathematics Pittsburg State University Pittsburg, KS 66762, U.S.A. and Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland and Division of Mathematics and Computer Science Faculty of Sciences Vrije Universiteit De Boelelaan 1081a 1081 HV Amsterdam, The Netherlands 
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Tadeusz Dobrowolski; Witold Marciszewski. Failure of the Factor Theorem for Borel pre-Hilbert spaces. Fundamenta Mathematicae, Tome 175 (2002) no. 1, pp. 53-68. doi: 10.4064/fm175-1-3

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