Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Schröder, Matthias http://www.dagstuhl.de/oasics License
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URN: urn:nbn:de:0030-drops-22748
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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:OASIcs:2009:2274,
  author =	{Matthias Schr{\"o}der},
  title =	{{A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2274},
  URN =		{urn:nbn:de:0030-drops-22748},
  doi =		{http://dx.doi.org/10.4230/OASIcs.CCA.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: 2009


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