Failure of the Factor Theorem for Borel pre-Hilbert spaces

Volume 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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image