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Some hierarchies of QCB0-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

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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 25 , Special Issue 8: Computing with Infinite Data: Topological and Logical Foundations Part 2 , December 2015 , pp. 1799 - 1823
Copyright
Copyright © Cambridge University Press 2014 

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