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Some hierarchies of QCB 0-spaces

Published online by Cambridge University Press:  10 November 2014

MATTHIAS SCHRÖDER and
VICTOR SELIVANOV
MATTHIAS SCHRÖDER
Affiliation:
University of the Bundeswehr Munich, Germany Email: matthias.schroeder@unibw.de
VICTOR SELIVANOV
Affiliation:
A.P. Ershov Institute of Informatics Systems SB RAS, Novisibirsk, Russia Email: vseliv@iis.nsk.su
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Abstract

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We define and study hierarchies of topological spaces induced by the classical Borel and Luzin hierarchies of sets. Our hierarchies are divided into two classes: hierarchies of countably based spaces induced by their embeddings into Pω, and hierarchies of spaces (not necessarily countably based) induced by their admissible representations. We concentrate on the non-collapse property of the hierarchies and on the relationships between hierarchies in the two classes.

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