Metrizability of Compact Sets in the Class \(\mathfrak {G}\)

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

Abstract

This chapter introduces (after Cascales and Orihuela) a large class of locally convex spaces under the name the class\(\mathfrak{G}\). The class \(\mathfrak{G}\) contains among others all (LM)-spaces (hence (LF)-spaces), and dual metric spaces (hence (DF)-spaces), spaces of distributions D′(Ω) and spaces A(Ω) of real analytic functions on open Ω⊂ℝ n . We show (following Cascales and Orihuela) that every precompact set in an lcs in the class \(\mathfrak{G}\) is metrizable. This general result covers many already known theorems for (DF)-spaces, (LF)-spaces and dual metric spaces.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Jerzy Kąkol
    • 1
  • 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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