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K-analytic Baire Spaces

  • Jerzy KąkolEmail author
  • Wiesław Kubiś
  • Manuel López-Pellicer
Part of the Developments in Mathematics book series (DEVM, volume 24)

Abstract

In this chapter, we show that a tvs that is a Baire space and admits a countably compact resolution is metrizable, separable and complete. We prove that a linear map T:EF from an F-space E having a resolution {K α :α∈ℕ} into a tvs F is continuous if each restriction T|K α is continuous. This theorem (due to Drewnowski) was motivated by the Arias–De Reina–Valdivia–Saxon theorem about non-Baire dense hyperplanes in Banach spaces. We provide a large class of weakly analytic metrizable and separable Baire tvs that are not analytic (clearly such spaces are necessarily not locally convex).

Keywords

Topological Space Polish Space Countable Basis Baire Space Baire Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Jerzy Kąkol
    • 1
    Email author
  • Wiesław Kubiś
    • 2
    • 3
  • Manuel López-Pellicer
    • 4
    • 5
  1. 1.Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznanPoland
  2. 2.Institute of MathematicsJan Kochanowski UniversityKielcePoland
  3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic
  4. 4.IUMPAUniversitat Poltècnica de ValènciaValenciaSpain
  5. 5.Royal Academy of SciencesMadridSpain

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