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DOI: 10.4230/OASIcs.CCA.2009.2274
URN: urn:nbn:de:0030-drops-22748
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2274/
Schröder, Matthias
Contributed Papers

A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)

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Abstract

We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces. We prove that the category $\QZ$ of quasi-zero-dimensional qcb$_0$-spaces is cartesian closed. Prominent examples of spaces in $\QZ$ are the spaces in the sequential hierarchy of the Kleene-Kreisel continuous functionals. Moreover, we characterise some types of closed subsets of $\QZ$-spaces in terms of their ability to allow extendability of continuous functions. These results are related to an open problem in Computable Analysis.

BibTeX - Entry

@InProceedings{schrder:DSP:2009:2274,
  author =	{Matthias Schr{\"o}der},
  title =	{A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)},
  booktitle =	{6th Int'l Conf. on Computability and Complexity in Analysis},
  year =	{2009},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2274},
  annote =	{Keywords: Computable analysis, Qcb-spaces, extendability},
}

Keywords: Computable analysis, Qcb-spaces, extendability
Seminar: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue date: 2009
Date of publication: 25.11.2009

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