Failure of the Factor Theorem for Borel pre-Hilbert spaces

Tom 175 / 2002

Tadeusz Dobrowolski, Witold Marciszewski Fundamenta Mathematicae 175 (2002), 53-68 MSC: 57N17, 46C05. DOI: 10.4064/fm175-1-3


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.


  • Tadeusz DobrowolskiDepartment of Mathematics
    Pittsburg State University
    Pittsburg, KS 66762, U.S.A.
    Department of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.
  • Witold MarciszewskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    Division of Mathematics and Computer Science
    Faculty of Sciences
    Vrije Universiteit
    De Boelelaan 1081a
    1081 HV Amsterdam, The Netherlands

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