eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2009-11-25
233
244
10.4230/OASIcs.CCA.2009.2274
article
A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)
Schröder, Matthias
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.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol011-cca2009/OASIcs.CCA.2009.2274/OASIcs.CCA.2009.2274.pdf
Computable analysis
Qcb-spaces
extendability