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A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract) Schröder, Matthias Computable analysis Qcb-spaces extendability 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matthias Schröder 2009 Is Part Of OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.CCA.2009.2274 urn:nbn:de:0030-drops-22748 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2274 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode