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Web-Compact Spaces and Angelic Theorems

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

Abstract

This chapter deals with the class of angelic spaces, introduced by Fremlin, for which several variants of compactness coincide. A remarkable paper of Orihuela introduces a large class of topological spaces X (under the name web-compact) for which the space C p (X) is angelic. Orihuela’s theorem covers many already known partial results providing Eberlein–Šmulian-type results. Following Orihuela, we show that C p (X) is angelic if X is web-compact. This yields, in particular, Talagrand’s result stating that for a compact space X the space C p (X) is K-analytic if and only if C(X) is weakly K-analytic. We present some quantitative versions of Grothendieck’s characterization of the weak compactness for spaces C(X) (for compact Hausdorff spaces X) and quantitative versions of the classical Eberlein–Grothendieck and Krein–Šmulian theorems.

Keywords

Banach Space Topological Space Compact Space Weak Topology Cluster Point 
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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