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Towards a descriptive theory of cb0-spaces

Published online by Cambridge University Press:  09 June 2016

VICTOR SELIVANOV
VICTOR SELIVANOV*
Affiliation:
A.P. Ershov Institute of Informatics Systems SB RAS and Novosibirsk State University, Novosibirsk, Russia Email: vseliv@iis.nsk.su
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Abstract

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The paper tries to extend some results of the classical Descriptive Set Theory to as many countably based T 0-spaces (cb0-spaces) as possible. Along with extending some central facts about Borel, Luzin and Hausdorff hierarchies of sets we also consider the more general case of k-partitions. In particular, we investigate the difference hierarchy of k-partitions and the fine hierarchy closely related to the Wadge hierarchy.

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