K-analytic and Analytic Spaces Cp(X)

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


This chapter deals with K-analytic and analytic spaces C p (X). Some results due to Talagrand, Tkachuk, Velichko and Canela are presented. A remarkable theorem of Christensen stating that a metrizable and separable space X is σ-compact if and only if C p (X) is analytic is proved. We show that the analyticity of C p (X) for any X implies that X is σ-compact (Calbrix’s theorem). We show that C p (X) is K-analytic-framed in ℝ X if and only if C p (X) admits a bounded resolution. We also gather several equivalent conditions for spaces C p (X) to be Lindelöf spaces over locally compact groups X.


Topological Space Compact Subset Compact Group Compact Space Closed Subspace 
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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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