Base-Complexity Classifications of QCB\(_0\)-Spaces

  • Matthew de Brecht
  • Matthias Schröder
  • Victor Selivanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)

Abstract

We define and study new classifications of qcb\(_0\)-spaces based on the idea to measure the complexity of their bases. The new classifications complement those given by the hierarchies of qcb\(_0\)-spaces introduced in [7, 8] and provide new tools to investigate non-countably based qcb\(_0\)-spaces. As a by-product, we show that there is no universal qcb\(_0\)-space and establish several apparently new properties of the Kleene-Kreisel continuous functionals of countable types.

Keywords

QCB\(_0\)-spaces \(Y\)-based spaces Hyperspaces Scott topology Hyperprojective hierarchy Kleene-Kreisel continuous functionals 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Matthew de Brecht
    • 1
  • Matthias Schröder
    • 2
  • Victor Selivanov
    • 3
  1. 1.National Institute of Information and Communications Technology (NICT)Center for Information and Neural Networks (CiNet)OsakaJapan
  2. 2.Department of MathematicsTU DarmstadtDarmstadtGermany
  3. 3.A.P. Ershov Institute of Informatics Systems SB RASNovosibirskRussia

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