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Precompact Sets in (LM)-Spaces and Dual Metric Spaces

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

Abstract

This chapter presents unified and direct proofs of Pfister, Cascales and Orihuela and Valdivia’s theorems about metrizability of precompact sets in (LF)-spaces, (DF)-spaces and dual metric spaces, respectively. The proofs do not require the typical machinery of quasi-Suslin spaces, upper semicontinuous compact-valued maps and so on.

Keywords

Direct Proof Elementary Approach Countable Subset Descriptive Topology Convex Envelope 
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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