Acta Mathematica Hungarica

, Volume 118, Issue 1–2, pp 149–154 | Cite as

On quasi-Souslin Cc(X) spaces

Article

Abstract

We prove that the space Cc(X) of the real-valued continuous functions with the compact-open topology is quasi-Souslin iff it is K-analytic. This implies that Cc(X) is K-analytic iff it is dominated by the irrationals.

Key words and phrases

K-analytic space quasi-Souslin space domination by the irrationals 

2000 Mathematics Subject Classification

54C14 54D09 46A03 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. V. Arkhangel’skii, Topological Function Spaces, Math. and its Applications 78, Kluwer Academic Publishers (Dordrecht, Boston, London, 1992).Google Scholar
  2. [2]
    B. Cascales, On K-analytic locally convex spaces, Arch. Math., 49 (1987), 232–244.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    B. Cascales, and J. Orihuela, On compactness in locally convex spaces, Math. Z., 195 (1987), 365–381.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J. C. Ferrando, J. Kakol, M. López Pellicer, and S. Saxon, Quasi-Souslin weak duals, submitted.Google Scholar
  5. [5]
    M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. Math., 110 (1979), 407–438.CrossRefMathSciNetGoogle Scholar
  6. [6]
    V. V. Tkachuk, A space C p(X) is dominated by irrationals if and only if it is K-analytic, Acta Math. Hungar., 107 (2005), 253–265.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    M. Valdivia, Topics in Locally Convex Spaces, Notas de Matemática 67, North Holland (Amsterdam, New York, Oxford, 1982).MATHGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Centro de Investigación OperativaUniversidad Miguel HernándezElche (Alicante)Spain
  2. 2.Departmento de Matemática AplicadaUniversidad PolitécnicaValenciaSpain

Personalised recommendations