A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces

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 qcblt;sub>0lt;/sub>-spaces is cartesian closed. prominent examples of spaces in qz are the spaces of the kleene-kreisel continuous functionals equipped with the respective sequential topology. 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 a problem in computable analysis.