Base-complexity classifications of qcb₀-spaces1

Article type: Research Article

Authors: de Brecht, Matthew^a | Schröder, Matthias^b | Selivanov, Victor^c

Affiliations: [a] National Institute of Information and Communications Technology (NICT), Center for Information and Neural Networks (CiNet), Osaka, Japan. matthew@nict.go.jp | [b] Department of Mathematics, TU Darmstadt, Darmstadt, Germany. matthias.schroeder@cca-net.de | [c] A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia. vseliv@iis.nsk.su

Abstract: We define and study new classifications of qcb0-spaces based on the idea to measure the complexity of their bases. The new classifications complement those given by recently introduced hierarchies of qcb0-spaces and provide new tools to investigate non-countably based qcb0-spaces. As a by-product, we show that there is no universal qcb0-space and establish several new properties of the Kleene–Kreisel continuous functionals of countable types.

Keywords: qcb₀-spaces, Y-based spaces, hyperspaces, Scott topology, hyperprojective hierarchy, Kleene–Kreisel continuous functionals

DOI: 10.3233/COM-150044

Journal: Computability, vol. 5, no. 1, pp. 75-102, 2016