Author:
SCHRÖDER MATTHIAS,SELIVANOV VICTOR
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.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference27 articles.
1. Extended admissibility
2. de Brecht M. and Yamamoto A. (2009) Σ0 α -admissible representations (extended abstract). In: Bauer A. , Hertling P. and Ko K.-I (eds.) 6th international conference on computability and complexity in analysis. OASICS 11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
3. Normann D. (1999) The continuous functionals. In: Griffor E. R. (Ed.) Handbook of Computability Theory, 251–275.
4. Schröder M. (2003) Admissible Representations for Continuous Computations, Ph.D. Thesis, FernUniversität Hagen.
5. Filter spaces and continuous functionals
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