An Effective Tietze-Urysohn Theorem for QCB-Spaces

The tietze-urysohn theorem states that every continuous real-valued func- tion defined on a closed subspace of a normal space can be extended to a continuous function on the whole space. we prove an effective version of this theorem in the type two model of effectivity (tte). moreover, we introduce for qcb-spaces a slightly weaker notion of normality than the classical one and show that this property suffices to establish an extension theorem for continuous functions defined on functionally closed subspaces. qcb-spaces are known to form an important subcategory of the cat- egory top of topological spaces. qcb is cartesian closed in contrast to top.