Some Hierarchies of QCB_0-Spaces
Matthias Schroeder, Victor Selivanov

TL;DR
This paper introduces and analyzes hierarchies of topological spaces based on classical Borel and Luzin set hierarchies, focusing on their non-collapse properties and interrelations.
Contribution
It defines two classes of hierarchies for topological spaces, one for countably based spaces and another for more general spaces, and studies their structural properties.
Findings
Hierarchies do not collapse under certain conditions
Relationships between different hierarchy classes are established
Insights into the structure of QCB_0-spaces and their representations
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 the domain P\omega, 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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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic
