TY - JOUR

T1 - Base-complexity classifications of qcb0-spaces1

AU - De Brecht, Matthew

AU - Schröder, Matthias

AU - Selivanov, Victor

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - hyperprojective hierarchy

KW - hyperspaces

KW - Kleene-Kreisel continuous functionals

KW - qcb0-spaces

KW - Scott topology

KW - Y-based spaces

UR - http://www.scopus.com/inward/record.url?scp=85011110655&partnerID=8YFLogxK

U2 - 10.3233/COM-150044

DO - 10.3233/COM-150044

M3 - Article

AN - SCOPUS:85011110655

VL - 5

SP - 75

EP - 102

JO - Computability

JF - Computability

SN - 2211-3568

IS - 1

ER -