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K-analytic and Quasi-Suslin Spaces

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

Abstract

This chapter deals with the K-analyticity of a topological space E and the concept of a resolution generated on E (i.e., a family of sets {K α :α∈ℕ} such that \(E=\bigcup_{\alpha}K_{\alpha}\) and K α K β if αβ). Compact resolutions (i.e., resolutions {K α :α∈ℕ} whose members are compact sets) naturally appear in many situations in topology and functional analysis. Any K-analytic space admits a compact resolution, and for many topological spaces X the existence of such a resolution is enough for X to be K-analytic. Many of the ideas in the book are related to the concept of compact resolution. We gather some results, mostly due to Valdivia, about lcs’s admitting resolutions consisting of Banach discs and their relations with the closed graph theorems. We present Hurewicz and Alexandrov’s theorems as well as the Calbrix–Hurewicz theorem, which yields that a regular analytic space X is not σ-compact if and only if X contains a closed subset homeomorphic to ℕ.

Keywords

Topological Space Compact Subset Open Neighborhood Polish Space Countable Network 
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
  • 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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