Failure of the Factor Theorem for Borel pre-Hilbert spaces

• Autorzy: Tadeusz Dobrowolski , Witold Marciszewski
• Języki publikacji: EN

Abstrakty

EN

In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_{σδσ}$-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.

Kategorie tematyczne

• 57N17: Topology of topological vector spaces
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 1
• Strony: 53-68

Daty

wydano

2002

Twórcy

autor

Tadeusz Dobrowolski

• Department of Mathematics, Pittsburg State University, Pittsburg, KS 66762, U.S.A.
• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

autor

Witold Marciszewski

• Institute 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

Identyfikatory

DOI

10.4064/fm175-1-3